fluids.compressible module¶

Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fluids.compressible.T_critical_flow(T, k)[source]¶

Calculates critical flow temperature Tcf for a fluid with the given isentropic coefficient. Tcf is in a flow (with Ma=1) whose stagnation conditions are known. Normally used with converging/diverging nozzles.

\[\frac{T^*}{T_0} = \frac{2}{k+1}\]

Parameters:	T : float Stagnation temperature of a fluid with Ma=1 [K] k : float Isentropic coefficient []
Returns:	Tcf : float Critical flow temperature at Ma=1 [K]

Notes

Assumes isentropic flow.

References

[R200]

(1, 2) Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 12.4 in [R200]:

>>> T_critical_flow(473, 1.289)
413.2809086937528

fluids.compressible.P_critical_flow(P, k)[source]¶

Calculates critical flow pressure Pcf for a fluid with the given isentropic coefficient. Pcf is in a flow (with Ma=1) whose stagnation conditions are known. Normally used with converging/diverging nozzles.

\[\frac{P^*}{P_0} = \left(\frac{2}{k+1}\right)^{k/(k-1)}\]

Parameters:	P : float Stagnation pressure of a fluid with Ma=1 [Pa] k : float Isentropic coefficient []
Returns:	Pcf : float Critical flow pressure at Ma=1 [Pa]

Notes

Assumes isentropic flow.

References

[R201]

(1, 2) Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 12.4 in [R201]:

>>> P_critical_flow(1400000, 1.289)
766812.9022792266

fluids.compressible.is_critical_flow(P1, P2, k)[source]¶

Determines if a flow of a fluid driven by pressure gradient P1 - P2 is critical, for a fluid with the given isentropic coefficient. This function calculates critical flow pressure, and checks if this is larger than P2. If so, the flow is critical and choked.

Parameters:	P1: float Higher, source pressure [Pa] P2: float Lower, downstream pressure [Pa] k : float Isentropic coefficient []
Returns:	flowtype : bool True if the flow is choked; otherwise False

Notes

Assumes isentropic flow. Uses P_critical_flow function.

References

[R202]

API. 2014. API 520 - Part 1 Sizing, Selection, and Installation of Pressure-relieving Devices, Part I - Sizing and Selection, 9E.

Examples

Examples 1-2 from API 520.

>>> is_critical_flow(670E3, 532E3, 1.11)
False
>>> is_critical_flow(670E3, 101E3, 1.11)
True

fluids.compressible.stagnation_energy(V)[source]¶

Calculates the increase in enthalpy dH which is provided by a fluid’s velocity V.

\[\Delta H = \frac{V^2}{2}\]

Parameters:	V : float Velocity [m/s]
Returns:	dH : float Incease in enthalpy [J/kg]

Notes

The units work out. This term is pretty small, but not trivial.

References

[R203]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> stagnation_energy(125)
7812.5

fluids.compressible.P_stagnation(P, T, Tst, k)[source]¶

Calculates stagnation flow pressure Pst for a fluid with the given isentropic coefficient and specified stagnation temperature and normal temperature. Normally used with converging/diverging nozzles.

\[\frac{P_0}{P}=\left(\frac{T_0}{T}\right)^{\frac{k}{k-1}}\]

Parameters:	P : float Normal pressure of a fluid [Pa] T : float Normal temperature of a fluid [K] Tst : float Stagnation temperature of a fluid moving at a certain velocity [K] k : float Isentropic coefficient []
Returns:	Pst : float Stagnation pressure of a fluid moving at a certain velocity [Pa]

Notes

Assumes isentropic flow.

References

[R204]

(1, 2) Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 12-1 in [R204].

>>> P_stagnation(54050., 255.7, 286.8, 1.4)
80772.80495900588

fluids.compressible.T_stagnation(T, P, Pst, k)[source]¶

Calculates stagnation flow temperature Tst for a fluid with the given isentropic coefficient and specified stagnation pressure and normal pressure. Normally used with converging/diverging nozzles.

\[T=T_0\left(\frac{P}{P_0}\right)^{\frac{k-1}{k}}\]

Parameters:	T : float Normal temperature of a fluid [K] P : float Normal pressure of a fluid [Pa] Pst : float Stagnation pressure of a fluid moving at a certain velocity [Pa] k : float Isentropic coefficient []
Returns:	Tst : float Stagnation temperature of a fluid moving at a certain velocity [K]

Notes

Assumes isentropic flow.

References

[R205]

(1, 2) Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 12-1 in [R205].

>>> T_stagnation(286.8, 54050, 54050*8, 1.4)
519.5230938217768

fluids.compressible.T_stagnation_ideal(T, V, Cp)[source]¶

Calculates the ideal stagnation temperature Tst calculated assuming the fluid has a constant heat capacity Cp and with a specified velocity V and tempeature T.

\[T^* = T + \frac{V^2}{2C_p}\]

Parameters:	T : float Tempearture [K] V : float Velocity [m/s] Cp : float Ideal heat capacity [J/kg/K]
Returns:	Tst : float Stagnation temperature [J/kg]

References

[R206]

(1, 2) Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 12-1 in [R206].

>>> T_stagnation_ideal(255.7, 250, 1005.)
286.79452736318405

fluids.control_valve module¶

Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fluids.control_valve.cavitation_index(P1, P2, Psat)[source]¶

Calculates the cavitation index of a valve with upstream and downstream absolute pressures P1 and P2 for a fluid with a vapor pressure Psat.

\[\sigma = \frac{P_1 - P_{sat}}{P_1 - P_2}\]

Parameters:	P1 : float Absolute pressure upstream of the valve [Pa] P2 : float Absolute pressure downstream of the valve [Pa] Psat : float Saturation pressure of the liquid at inlet temperature [Pa]
Returns:	sigma : float Cavitation index of the valve [-]

Notes

Larger values are safer. Models for adjusting cavitation indexes provided by the manufacturer to the user’s conditions are available, making use of scaling the pressure differences and size differences.

Values can be calculated for incipient cavitation, constant cavitation, maximum vibration cavitation, incipient damage, and choking cavitation.

Has also been defined as:

\[\sigma = \frac{P_2 - P_{sat}}{P_1 - P_2}\]

Another definition and notation series is:

\[K = xF = \frac{1}{\sigma} = \frac{P_1 - P_2}{P_1 - P_{sat}}\]

References

[R207]

ISA. “RP75.23 Considerations for Evaluating Control Valve Cavitation.” 1995.

Examples

>>> cavitation_index(1E6, 8E5, 2E5)
4.0

fluids.control_valve.size_control_valve_l(rho, Psat, Pc, mu, P1, P2, Q, D1, D2, d, FL, Fd)[source]¶

Calculates flow coefficient of a control valve passing a liquid according to IEC 60534. Uses a large number of inputs in SI units. Note the return value is not standard SI. All parameters are required. This sizing model does not officially apply to liquid mixtures, slurries, non-Newtonian fluids, or liquid-solid conveyance systems. For details of the calculations, consult [R208].

Parameters:

rho : float Density of the liquid at the inlet [kg/m^3] Psat : float Saturation pressure of the fluid at inlet temperature [Pa] Pc : float Critical pressure of the fluid [Pa] mu : float Viscosity of the fluid [Pa*s] P1 : float Inlet pressure of the fluid before valves and reducers [Pa] P2 : float Outlet pressure of the fluid after valves and reducers [Pa] Q : float Volumetric flow rate of the fluid [m^3/s] D1 : float Diameter of the pipe before the valve [m] D2 : float Diameter of the pipe after the valve [m] d : float Diameter of the valve [m] FL : float Liquid pressure recovery factor of a control valve without attached fittings [] Fd : float Valve style modifier []

Returns:

C : float Kv flow coefficient [m^3/hr at a dP of 1 bar]

References

[R208]

(1, 2, 3, 4) IEC 60534-2-1 / ISA-75.01.01-2007

Examples

From [R208], matching example 1 for a globe, parabolic plug, flow-to-open valve.

>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-4,
... P1=680E3, P2=220E3, Q=0.1, D1=0.15, D2=0.15, d=0.15,
... FL=0.9, Fd=0.46)
164.9954763704956

From [R208], matching example 2 for a ball, segmented ball, flow-to-open valve.

>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-4,
... P1=680E3, P2=220E3, Q=0.1, D1=0.1, D2=0.1, d=0.1,
... FL=0.6, Fd=0.98)
238.05817216710483

Modified example 1 with non-choked flow, with reducer and expander

>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-4,
...  P1=680E3, P2=220E3, Q=0.1, D1=0.1, D2=0.09, d=0.08, FL=0.9, Fd=0.46)
177.44417090966715

Modified example 2 with non-choked flow, with reducer and expander

>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-4,
... P1=680E3, P2=220E3, Q=0.1, D1=0.1, D2=0.1, d=0.95, FL=0.6, Fd=0.98)
230.1734424266345

Modified example 2 with laminar flow at 100x viscosity, 100th flow rate, and 1/10th diameters:

>>> size_control_valve_l(rho=965.4, Psat=70.1E3, Pc=22120E3, mu=3.1472E-2,
... P1=680E3, P2=220E3, Q=0.001, D1=0.01, D2=0.01, d=0.01, FL=0.6, Fd=0.98)
3.0947562381723626

fluids.control_valve.size_control_valve_g(T, MW, mu, gamma, Z, P1, P2, Q, D1, D2, d, FL, Fd, xT)[source]¶

Calculates flow coefficient of a control valve passing a gas according to IEC 60534. Uses a large number of inputs in SI units. Note the return value is not standard SI. All parameters are required. For details of the calculations, consult [R209]. Note the inlet gas flow conditions.

Parameters:

T : float Temperature of the gas at the inlet [K] MW : float Molecular weight of the gas [g/mol] mu : float Viscosity of the fluid at inlet conditions [Pa*s] gamma : float Specific heat capacity ratio [-] Z : float Compressibility factor at inlet conditions, [-] P1 : float Inlet pressure of the gas before valves and reducers [Pa] P2 : float Outlet pressure of the gas after valves and reducers [Pa] Q : float Volumetric flow rate of the gas at 273.15 K and 1 atm specifically [m^3/s] D1 : float Diameter of the pipe before the valve [m] D2 : float Diameter of the pipe after the valve [m] d : float Diameter of the valve [m] FL : float Liquid pressure recovery factor of a control valve without attached fittings [] Fd : float Valve style modifier [] xT : float Pressure difference ratio factor of a valve without fittings at choked flow [-]

Returns:

C : float Kv flow coefficient [m^3/hr at a dP of 1 bar]

References

[R209]

(1, 2, 3, 4) IEC 60534-2-1 / ISA-75.01.01-2007

Examples

From [R209], matching example 3 for non-choked gas flow with attached fittings and a rotary, eccentric plug, flow-to-open control valve:

>>> size_control_valve_g(T=433., MW=44.01, mu=1.4665E-4, gamma=1.30,
... Z=0.988, P1=680E3, P2=310E3, Q=38/36., D1=0.08, D2=0.1, d=0.05,
... FL=0.85, Fd=0.42, xT=0.60)
72.58664545391052

From [R209], roughly matching example 4 for a small flow trim sized tapered needle plug valve. Difference is 3% and explained by the difference in algorithms used.

>>> size_control_valve_g(T=320., MW=39.95, mu=5.625E-5, gamma=1.67, Z=1.0,
... P1=2.8E5, P2=1.3E5, Q=0.46/3600., D1=0.015, D2=0.015, d=0.015, FL=0.98,
... Fd=0.07, xT=0.8)
0.016498765335995726

fluids.core module¶

Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fluids.core.Reynolds(V, D, rho=None, mu=None, nu=None)[source]¶

Calculates Reynolds number or Re for a fluid with the given properties for the specified velocity and diameter.

\[Re = {D \cdot V}{\nu} = \frac{\rho V D}{\mu}\]

Inputs either of any of the following sets:

• V, D, density rho and kinematic viscosity mu
• V, D, and dynamic viscosity nu

Parameters:	D : float Diameter [m] V : float Velocity [m/s] rho : float, optional Density, [kg/m^3] mu : float, optional Dynamic viscosity, [Pa*s] nu : float, optional Kinematic viscosity, [m^2/s]
Returns:	Re : float Reynolds number []

Notes

\[Re = \frac{\text{Momentum}}{\text{Viscosity}}\]

An error is raised if none of the required input sets are provided.

References

[R210]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R211]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Reynolds(2.5, 0.25, 1.1613, 1.9E-5)
38200.65789473684
>>> Reynolds(2.5, 0.25, nu=1.636e-05)
38202.93398533008

fluids.core.Prandtl(Cp=None, k=None, mu=None, nu=None, rho=None, alpha=None)[source]¶

Calculates Prandtl number or Pr for a fluid with the given parameters.

\[Pr = \frac{C_p \mu}{k} = \frac{\nu}{\alpha} = \frac{C_p \rho \nu}{k}\]

Inputs can be any of the following sets:

• Heat capacity, dynamic viscosity, and thermal conductivity
• Thermal diffusivity and kinematic viscosity
• Heat capacity, kinematic viscosity, thermal conductivity, and density

Parameters:	Cp : float Heat capacity, [J/kg/K] k : float Thermal conductivity, [W/m/K] mu : float, optional Dynamic viscosity, [Pa*s] nu : float, optional Kinematic viscosity, [m^2/s] rho : float Density, [kg/m^3] alpha : float Thermal diffusivity, [m^2/s]
Returns:	Pr : float Prandtl number []

Notes

\[Pr=\frac{\text{kinematic viscosity}}{\text{thermal diffusivity}} = \frac{\text{momentum diffusivity}}{\text{thermal diffusivity}}\]

An error is raised if none of the required input sets are provided.

References

[R212]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R213]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

[R214]

Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

Examples

>>> Prandtl(Cp=1637., k=0.010, mu=4.61E-6)
0.754657
>>> Prandtl(Cp=1637., k=0.010, nu=6.4E-7, rho=7.1)
0.7438528
>>> Prandtl(nu=6.3E-7, alpha=9E-7)
0.7000000000000001

fluids.core.Grashof(L, beta, T1, T2=0, rho=None, mu=None, nu=None, g=9.80665)[source]¶

Calculates Grashof number or Gr for a fluid with the given properties, temperature difference, and characteristic length.

\[Gr = \frac{g\beta (T_s-T_\infty)L^3}{\nu^2} = \frac{g\beta (T_s-T_\infty)L^3\rho^2}{\mu^2}\]

Inputs either of any of the following sets:

• L, beta, T1 and T2, and density rho and kinematic viscosity mu
• L, beta, T1 and T2, and dynamic viscosity nu

Parameters:

L : float Characteristic length [m] beta : float Volumetric thermal expansion coefficient [1/K] T1 : float Temperature 1, usually a film temperature [K] T2 : float, optional Temperature 2, usually a bulk temperature (or 0 if only a difference is provided to the function) [K] rho : float, optional Density, [kg/m^3] mu : float, optional Dynamic viscosity, [Pa*s] nu : float, optional Kinematic viscosity, [m^2/s] g : float, optional Acceleration due to gravity, [m/s^2]

Returns:

Gr : float Grashof number []

Notes

\[Gr = \frac{\text{Buoyancy forces}}{\text{Viscous forces}}\]

An error is raised if none of the required input sets are provided. Used in free convection problems only.

References

[R215]

(1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R216]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 4 of [R215], p. 1-21 (matches):

>>> Grashof(L=0.9144, beta=0.000933, T1=178.2, rho=1.1613, mu=1.9E-5)
4656936556.178915
>>> Grashof(L=0.9144, beta=0.000933, T1=378.2, T2=200, nu=1.636e-05)
4657491516.530312

fluids.core.Nusselt(h, L, k)[source]¶

Calculates Nusselt number Nu for a heat transfer coefficient h, characteristic length L, and thermal conductivity k.

\[Nu = \frac{hL}{k}\]

Parameters:	h : float Heat transfer coefficient, [W/m^2/K] L : float Characteristic length, no typical definition [m] k : float Thermal conductivity of fluid [W/m/K]
Returns:	Nu : float Nusselt number, [-]

Notes

Do not confuse k, the thermal conductivity of the fluid, with that of within a solid object associated with!

\[Nu = \frac{\text{Convective heat transfer}} {\text{Conductive heat transfer}}\]

References

[R217]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R218]

Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

Examples

>>> Nusselt(1000., 1.2, 300.)
4.0
>>> Nusselt(10000., .01, 4000.)
0.025

fluids.core.Sherwood(K, L, D)[source]¶

Calculates Sherwood number Sh for a mass transfer coefficient K, characteristic length L, and diffusivity D.

\[Sh = \frac{KL}{D}\]

Parameters:	K : float Mass transfer coefficient, [m/s] L : float Characteristic length, no typical definition [m] D : float Diffusivity of a species [m/s^2]
Returns:	Sh : float Sherwood number, [-]

Notes

\[Sh = \frac{\text{Mass transfer by convection}} {\text{Mass transfer by diffusion}} = \frac{K}{D/L}\]

References

[R219]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Sherwood(1000., 1.2, 300.)
4.0

fluids.core.Rayleigh(Pr, Gr)[source]¶

Calculates Rayleigh number or Ra using Prandtl number Pr and Grashof number Gr for a fluid with the given properties, temperature difference, and characteristic length used to calculate Gr and Pr.

\[Ra = PrGr\]

Parameters:	Pr : float Prandtl number [] Gr : float Grashof number []
Returns:	Ra : float Rayleigh number []

Notes

Used in free convection problems only.

References

[R220]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R221]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Rayleigh(1.2, 4.6E9)
5520000000.0

fluids.core.Schmidt(D, mu=None, nu=None, rho=None)[source]¶

Calculates Schmidt number or Sc for a fluid with the given parameters.

\[Sc = \frac{\mu}{D\rho} = \frac{\nu}{D}\]

Inputs can be any of the following sets:

• Diffusivity, dynamic viscosity, and density
• Diffusivity and kinematic viscosity

Parameters:	D : float Diffusivity of a species, [m^2/s] mu : float, optional Dynamic viscosity, [Pa*s] nu : float, optional Kinematic viscosity, [m^2/s] rho : float, optional Density, [kg/m^3]
Returns:	Sc : float Schmidt number []

Notes

\[Sc =\frac{\text{kinematic viscosity}}{\text{molecular diffusivity}} = \frac{\text{viscous diffusivity}}{\text{species diffusivity}}\]

An error is raised if none of the required input sets are provided.

References

[R222]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R223]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Schmidt(D=2E-6, mu=4.61E-6, rho=800)
0.00288125
>>> Schmidt(D=1E-9, nu=6E-7)
599.9999999999999

fluids.core.Peclet_heat(V, L, rho=None, Cp=None, k=None, alpha=None)[source]¶

Calculates heat transfer Peclet number or Pe for a specified velocity V, characteristic length L, and specified properties for the given fluid.

\[Pe = \frac{VL\rho C_p}{k} = \frac{LV}{\alpha}\]

Inputs either of any of the following sets:

• V, L, density rho, heat capcity Cp, and thermal conductivity k
• V, L, and thermal diffusivity alpha

Parameters:	V : float Velocity [m/s] L : float Characteristic length [m] rho : float, optional Density, [kg/m^3] Cp : float, optional Heat capacity, [J/kg/K] k : float, optional Thermal conductivity, [W/m/K] alpha : float, optional Thermal diffusivity, [m^2/s]
Returns:	Pe : float Peclet number (heat) []

Notes

\[Pe = \frac{\text{Bulk heat transfer}}{\text{Conduction heat transfer}}\]

An error is raised if none of the required input sets are provided.

References

[R224]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R225]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Peclet_heat(1.5, 2, 1000., 4000., 0.6)
20000000.0
>>> Peclet_heat(1.5, 2, alpha=1E-7)
30000000.0

fluids.core.Peclet_mass(V, L, D)[source]¶

Calculates mass transfer Peclet number or Pe for a specified velocity V, characteristic length L, and diffusion coefficient D.

\[Pe = \frac{L V}{D}\]

Parameters:	V : float Velocity [m/s] L : float Characteristic length [m] D : float Diffusivity of a species, [m^2/s]
Returns:	Pe : float Peclet number (mass) []

Notes

\[Pe = \frac{\text{Advective transport rate}}{\text{Diffusive transport rate}}\]

References

[R226]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Peclet_mass(1.5, 2, 1E-9)
3000000000.0

fluids.core.Fourier_heat(t, L, rho=None, Cp=None, k=None, alpha=None)[source]¶

Calculates heat transfer Fourier number or Fo for a specified time t, characteristic length L, and specified properties for the given fluid.

\[Fo = \frac{k t}{C_p \rho L^2} = \frac{\alpha t}{L^2}\]

Inputs either of any of the following sets:

• t, L, density rho, heat capcity Cp, and thermal conductivity k
• t, L, and thermal diffusivity alpha

Parameters:	t : float time [s] L : float Characteristic length [m] rho : float, optional Density, [kg/m^3] Cp : float, optional Heat capacity, [J/kg/K] k : float, optional Thermal conductivity, [W/m/K] alpha : float, optional Thermal diffusivity, [m^2/s]
Returns:	Fo : float Fourier number (heat) []

Notes

\[Fo = \frac{\text{Heat conduction rate}} {\text{Rate of thermal energy storage in a solid}}\]

An error is raised if none of the required input sets are provided.

References

[R227]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R228]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Fourier_heat(1.5, 2, 1000., 4000., 0.6)
5.625e-08
>>> Fourier_heat(1.5, 2, alpha=1E-7)
3.75e-08

fluids.core.Fourier_mass(t, L, D)[source]¶

Calculates mass transfer Fourier number or Fo for a specified time t, characteristic length L, and diffusion coefficient D.

\[Fo = \frac{D t}{L^2}\]

Parameters:	t : float time [s] L : float Characteristic length [m] D : float Diffusivity of a species, [m^2/s]
Returns:	Fo : float Fourier number (mass) []

Notes

\[Fo = \frac{\text{Diffusive transport rate}}{\text{Storage rate}}\]

References

[R229]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Fourier_mass(1.5, 2, 1E-9)
3.7500000000000005e-10

fluids.core.Graetz_heat(V, D, x, rho=None, Cp=None, k=None, alpha=None)[source]¶

Calculates Graetz number or Gz for a specified velocity V, diameter D, axial diatance x, and specified properties for the given fluid.

\[Gz = \frac{VD^2\cdot C_p \rho}{x\cdot k} = \frac{VD^2}{x \alpha}\]

Inputs either of any of the following sets:

• V, D, x, density rho, heat capcity Cp, and thermal conductivity k
• V, D, x, and thermal diffusivity alpha

Parameters:	V : float Velocity, [m/s] D : float Diameter [m] x : float Axial distance [m] rho : float, optional Density, [kg/m^3] Cp : float, optional Heat capacity, [J/kg/K] k : float, optional Thermal conductivity, [W/m/K] alpha : float, optional Thermal diffusivity, [m^2/s]
Returns:	Gz : float Graetz number []

Notes

\[Gz = \frac{\text{Time for radial heat diffusion in a fluid by conduction}} {\text{Time taken by fluid to reach distance x}}\]\[Gz = \frac{D}{x}RePr\]

An error is raised if none of the required input sets are provided.

References

[R230]

Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

Examples

>>> Graetz_heat(1.5, 0.25, 5, 800., 2200., 0.6)
55000.0
>>> Graetz_heat(1.5, 0.25, 5, alpha=1E-7)
187500.0

fluids.core.Lewis(D=None, alpha=None, Cp=None, k=None, rho=None)[source]¶

Calculates Lewis number or Le for a fluid with the given parameters.

\[Le = \frac{k}{\rho C_p D} = \frac{\alpha}{D}\]

Inputs can be either of the following sets:

• Diffusivity and Thermal diffusivity
• Diffusivity, heat capacity, thermal conductivity, and density

Parameters:	D : float Diffusivity of a species, [m^2/s] alpha : float, optional Thermal diffusivity, [m^2/s] Cp : float, optional Heat capacity, [J/kg/K] k : float, optional Thermal conductivity, [W/m/K] rho : float, optional Density, [kg/m^3]
Returns:	Le : float Lewis number []

Notes

\[Le=\frac{\text{Thermal diffusivity}}{\text{Mass diffusivity}} = \frac{Sc}{Pr}\]

An error is raised if none of the required input sets are provided.

References

[R231]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R232]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

[R233]

Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

Examples

>>> Lewis(D=22.6E-6, alpha=19.1E-6)
0.8451327433628318
>>> Lewis(D=22.6E-6, rho=800., k=.2, Cp=2200)
0.00502815768302494

fluids.core.Weber(V, L, rho, sigma)[source]¶

Calculates Weber number, We, for a fluid with the given density, surface tension, velocity, and geometric parameter (usually diameter of bubble).

\[We = \frac{V^2 L\rho}{\sigma}\]

Parameters:	V : float Velocity of fluid, [m/s] L : float Characteristic length, typically bubble diameter [m] rho : float Density of fluid, [kg/m^3] sigma : float Surface tension, [N/m]
Returns:	We : float Weber number []

Notes

Used in bubble calculations.

\[We = \frac{\text{inertial force}}{\text{surface tension force}}\]

References

[R234]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R235]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

[R236]

Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

Examples

>>> Weber(V=0.18, L=0.001, rho=900., sigma=0.01)
2.916

fluids.core.Mach(V, c)[source]¶

Calculates Mach number or Ma for a fluid of velocity V with speed of sound c.

\[Ma = \frac{V}{c}\]

Parameters:	V : float Velocity of fluid, [m/s] c : float Speed of sound in fluid, [m/s]
Returns:	Ma : float Mach number []

Notes

Used in compressible flow calculations.

\[Ma = \frac{\text{fluid velocity}}{\text{sonic velocity}}\]

References

[R237]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R238]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Mach(33., 330)
0.1

fluids.core.Knudsen(path, L)[source]¶

Calculates Knudsen number or Kn for a fluid with mean free path path and for a characteristic length L.

\[Kn = \frac{\lambda}{L}\]

Parameters:	path : float Mean free path between molecular collisions, [m] L : float Characteristic length, [m]
Returns:	Kn : float Knudsen number []

Notes

Used in mass transfer calculations.

\[Kn = \frac{\text{Mean free path length}}{\text{Characteristic length}}\]

References

[R239]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R240]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Knudsen(1e-10, .001)
1e-07

fluids.core.Bond(rhol, rhog, sigma, L)[source]¶

Calculates Bond number, Bo also known as Eotvos number, for a fluid with the given liquid and gas densities, surface tension, and geometric parameter (usually length).

\[Bo = \frac{g(\rho_l-\rho_g)L^2}{\sigma}\]

Parameters:	rhol : float Density of liquid, [kg/m^3] rhog : float Density of gas, [kg/m^3] sigma : float Surface tension, [N/m] L : float Characteristic length, [m]
Returns:	Bo : float Bond number []

References

[R241]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Bond(1000., 1.2, .0589, 2)
665187.2339558573

fluids.core.Froude(V, L, g=9.80665, squared=False)[source]¶

Calculates Froude number Fr for velocity V and geometric length L. If desired, gravity can be specified as well. Normally the function returns the result of the equation below; Froude number is also often said to be defined as the square of the equation below.

\[Fr = \frac{V}{\sqrt{gL}}\]

Parameters:	V : float Velocity of the particle or fluid, [m/s] L : float Characteristic length, no typical definition [m] g : float, optional Acceleration due to gravity, [m/s^2] squared : bool, optional Whether to return the squared form of Frounde number
Returns:	Fr : float Froude number, [-]

Notes

Many alternate definitions including density ratios have been used.

\[Fr = \frac{\text{Inertial Force}}{\text{Gravity Force}}\]

References

[R242]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R243]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Froude(1.83, L=2., g=1.63)
1.0135432593877318
>>> Froude(1.83, L=2., squared=True)
0.17074638128208924

fluids.core.Strouhal(f, L, V)[source]¶

Calculates Strouhal number St for a characteristic frequency f, characteristic length L, and velocity V.

\[St = \frac{fL}{V}\]

Parameters:	f : float Characteristic frequency, usually that of vortex shedding, [Hz] L : float Characteristic length, [m] V : float Velocity of the fluid, [m/s]
Returns:	St : float Strouhal number, [-]

Notes

Sometimes abbreviated to S or Sr.

\[St = \frac{\text{Characteristif flow time}} {\text{Period of oscillation}}\]

References

[R244]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R245]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Strouhal(8, 2., 4.)
4.0

fluids.core.Biot(h, L, k)[source]¶

Calculates Biot number Br for heat transfer coefficient h, geometric length L, and thermal conductivity k.

\[Bi=\frac{hL}{k}\]

Parameters:	h : float Heat transfer coefficient, [W/m^2/K] L : float Characteristic length, no typical definition [m] k : float Thermal conductivity, within the object [W/m/K]
Returns:	Bi : float Biot number, [-]

Notes

Do not confuse k, the thermal conductivity within the object, with that of the medium h is calculated with!

\[Bi = \frac{\text{Surface thermal resistance}} {\text{Internal thermal resistance}}\]

References

[R246]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R247]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Biot(1000., 1.2, 300.)
4.0
>>> Biot(10000., .01, 4000.)
0.025

fluids.core.Stanton(h, V, rho, Cp)[source]¶

Calculates Stanton number or St for a specified heat transfer coefficient h, velocity V, density rho, and heat capacity Cp.

\[St = \frac{h}{V\rho Cp}\]

Parameters:	h : float Heat transfer coefficient, [W/m^2/K] V : float Velocity, [m/s] rho : float Density, [kg/m^3] Cp : float Heat capacity, [J/kg/K]
Returns:	St : float Stanton number []

Notes

\[St = \frac{\text{Heat transfer coefficient}}{\text{Thermal capacity}}\]

References

[R248]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R248]

Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

Examples

>>> Stanton(5000, 5, 800, 2000.)
0.000625

fluids.core.Euler(dP, rho, V)[source]¶

Calculates Euler number or Eu for a fluid of velocity V and density rho experiencing a pressure drop dP.

\[Eu = \frac{\Delta P}{\rho V^2}\]

Parameters:	dP : float Pressure drop experience by the fluid, [Pa] rho : float Density of the fluid, [kg/m^3] V : float Velocity of fluid, [m/s]
Returns:	Eu : float Euler number []

Notes

Used in pressure drop calculations. Rarely, this number is divided by two. Named after Leonhard Euler applied calculus to fluid dynamics.

\[Eu = \frac{\text{Pressure drop}}{2\cdot \text{velocity head}}\]

References

[R250]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R251]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Euler(1E5, 1000., 4)
6.25

fluids.core.Cavitation(P, Psat, rho, V)[source]¶

Calculates Cavitation number or Ca for a fluid of velocity V with a pressure P, vapor pressure Psat, and density rho.

\[Ca = \sigma_c = \sigma = \frac{P-P_{sat}}{\frac{1}{2}\rho V^2}\]

Parameters:	P : float Internal pressure of the fluid, [Pa] Psat : float Vapor pressure of the fluid, [Pa] rho : float Density of the fluid, [kg/m^3] V : float Velocity of fluid, [m/s]
Returns:	Ca : float Cavitation number []

Notes

Used in determining if a flow through a restriction will cavitate. Sometimes, the multiplication by 2 will be omitted;

\[Ca = \frac{\text{Pressure - Vapor pressure}} {\text{Inertial pressure}}\]

References

[R252]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R253]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Cavitation(2E5, 1E4, 1000, 10)
3.8

fluids.core.Eckert(V, Cp, dT)[source]¶

Calculates Eckert number or Ec for a fluid of velocity V with a heat capacity Cp, between two temperature given as dT.

\[Ec = \frac{V^2}{C_p \Delta T}\]

Parameters:	V : float Velocity of fluid, [m/s] Cp : float Heat capacity of the fluid, [J/kg/K] dT : float Temperature difference, [K]
Returns:	Ec : float Eckert number []

Notes

Used in certain heat transfer calculations. Fairly rare.

\[Ec = \frac{\text{Kinetic energy} }{ \text{Enthalpy difference}}\]

References

[R254]

Goldstein, Richard J. ECKERT NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.e.eckert_number

Examples

>>> Eckert(10, 2000., 25.)
0.002

fluids.core.Jakob(Cp, Hvap, Te)[source]¶

Calculates Jakob number or Ja for a boiling fluid with sensible heat capacity Cp, enthalpy of vaporization Hvap, and boiling at Te degrees above its saturation boiling point.

\[Ja = \frac{C_{P}\Delta T_e}{\Delta H_{vap}}\]

Parameters:	Cp : float Heat capacity of the fluid, [J/kg/K] Hvap : float Enthalpy of vaporization of the fluid at its saturation temperature [J/kg] Te : float Temperature difference above the fluid’s saturation boiling temperature, [K]
Returns:	Ja : float Jakob number []

Notes

Used in boiling heat transfer analysis. Fairly rare.

\[Ja = \frac{\Delta \text{Sensible heat}}{\Delta \text{Latent heat}}\]

References

[R255]

Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.

[R256]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Jakob(4000., 2E6, 10.)
0.02

fluids.core.Power_number(P, L, N, rho)[source]¶

Calculates power number, Po, for an agitator applying a specified power P with a characteristic length L, rotationa speed N, to a fluid with a specified density rho.

\[Po = \frac{P}{\rho N^3 D^5}\]

Parameters:	P : float Power applied, [W] L : float Characteristic length, typically agitator diameter [m] N : float Speed [revolutions/second] rho : float Density of fluid, [kg/m^3]
Returns:	Po : float Power number []

Notes

Used in mixing calculations.

\[Po = \frac{\text{Power}}{\text{Rotational inertia}}\]

References

[R257]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R258]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Power_number(P=180, L=0.01, N=2.5, rho=800.)
144000000.0

fluids.core.Drag(F, A, V, rho)[source]¶

Calculates drag coefficient Cd for a given drag force F, projected area A, characteristic velocity V, and density rho.

\[C_D = \frac{F_d}{A\cdot\frac{1}{2}\rho V^2}\]

Parameters:	F : float Drag force, [N] A : float Projected area, [m^2] V : float Characteristic velocity, [m/s] rho : float Density, [kg/m^3]
Returns:	Cd : float Drag coefficient, [-]

Notes

Used in flow around objects, or objects flowing within a fluid.

\[C_D = \frac{\text{Drag forces}}{\text{Projected area}\cdot \text{Velocity head}}\]

References

[R259]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R260]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Drag(1000, 0.0001, 5, 2000)
400.0

fluids.core.Capillary(V, mu, sigma)[source]¶

Calculates Capillary number Ca for a characteristic velocity V, viscosity mu, and surface tension sigma.

\[Ca = \frac{V \mu}{\sigma}\]

Parameters:	V : float Characteristic velocity, [m/s] mu : float Dynamic viscosity, [Pa*s] sigma : float Surface tension, [N/m]
Returns:	Ca : float Capillary number, [-]

Notes

Used in porous media calculations and film flow calculations. Surface tension may gas-liquid, or liquid-liquid.

\[Ca = \frac{\text{Viscous forces}} {\text{Surface forces}}\]

References

[R261]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R262]

Kundu, Pijush K., Ira M. Cohen, and David R. Dowling. Fluid Mechanics. Academic Press, 2012.

Examples

>>> Capillary(1.2, 0.01, .1)
0.12

fluids.core.Archimedes(L, rhof, rhop, mu, g=9.80665)[source]¶

Calculates Archimedes number, Ar, for a fluid and particle with the given densities, characteristic length, viscosity, and gravity (usually diameter of particle).

\[Ar = \frac{L^3 \rho_f(\rho_p-\rho_f)g}{\mu^2}\]

Parameters:	L : float Characteristic length, typically particle diameter [m] rhof : float Density of fluid, [kg/m^3] rhop : float Density of particle, [kg/m^3] mu : float Viscosity of fluid, [N/m] g : float, optional Acceleration due to gravity, [m/s^2]
Returns:	Ar : float Archimedes number []

Notes

Used in fluid-particle interaction calculations.

\[Ar = \frac{\text{Gravitational force}}{\text{Viscous force}}\]

References

[R263]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R264]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Archimedes(0.002, 0.2804, 2699.37, 4E-5)
37109.575890227665

fluids.core.Ohnesorge(L, rho, mu, sigma)[source]¶

Calculates Ohnesorge number, Oh, for a fluid with the given characteristic length, density, viscosity, and surface tension.

\[\text{Oh} = \frac{\mu}{\sqrt{\rho \sigma L }}\]

Parameters:	L : float Characteristic length [m] rho : float Density of fluid, [kg/m^3] mu : float Viscosity of fluid, [Pa*s] sigma : float Surface tension, [N/m]
Returns:	Oh : float Ohnesorge number []

Notes

Often used in spray calculations. Sometimes given the symbol Z.

\[Oh = \frac{\sqrt{\text{We}}}{\text{Re}}= \frac{\text{viscous forces}} {\sqrt{\text{Inertia}\cdot\text{Surface tension}} }\]

References

[R265]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Ohnesorge(1E-5, 2000., 1E-4, 1E-1)
0.00223606797749979

fluids.core.thermal_diffusivity(k, rho, Cp)[source]¶

Calculates thermal diffusivity or alpha for a fluid with the given parameters.

\[\alpha = \frac{k}{\rho Cp}\]

Parameters:	k : float Thermal conductivity, [W/m/K] Cp : float Heat capacity, [J/kg/K] rho : float Density, [kg/m^3]
Returns:	alpha : float Thermal diffusivity, [m^2/s]

References

[R266]

Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> thermal_diffusivity(0.02, 1., 1000.)
2e-05

fluids.core.c_ideal_gas(T, k, MW)[source]¶

Calculates speed of sound c in an ideal gas at tempereture T.

\[c = \sqrt{kR_{specific}T}\]

Parameters:	T : float Temperature of fluid, [K] k : float Isentropic exponent of fluid, [-] MW : float Molecular weight of fluid, [g/mol]
Returns:	c : float Speed of sound in fluid, [m/s]

Notes

Used in compressible flow calculations. Note that the gas constant used is the specific gas constant:

\[R_{specific} = R\frac{1000}{MW}\]

References

[R267]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R268]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> c_ideal_gas(1.4, 303., 28.96)
348.9820361755092

fluids.core.relative_roughness(D, roughness=1.52e-06)[source]¶

Calculates relative roughness eD using a diameter and the roughness of the material of the wall. Default roughness is that of steel.

\[eD=\frac{\epsilon}{D}\]

Parameters:	D : float Diameter of pipe, [m] roughness : float, optional Roughness of pipe wall [m]
Returns:	eD : float Relative Roughness, [-]

References

[R269]

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

[R270]

Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> relative_roughness(0.0254)
5.9842519685039374e-05
>>> relative_roughness(0.5, 1E-4)
0.0002

fluids.core.nu_mu_converter(rho, nu=0, mu=0)[source]¶

Specify density and either Kinematic viscosity or Dynamic Viscosity by name for the result to be converted to the other.

>>> nu_mu_converter(998.1,nu=1.01E-6)
0.001008081

fluids.core.gravity(latitude, height)[source]¶

Calculates local acceleration due to gravity g according to [R271]. Uses latitude and height to calculate g.

\[g = 9.780356(1 + 0.0052885\sin^2\phi - 0.0000059^22\phi) - 3.086\times 10^{-6} H\]

Parameters:	latitude : float Degrees, [degrees] height : float Height above earth’s surface [m]
Returns:	g : float Acceleration due to gravity, [m/s^2]

Notes

Better models, such as EGM2008 exist.

References

[R271]

(1, 2) Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014.

Examples

>>> gravity(55, 1E4)
9.784151976863571

fluids.core.K_from_f(f, L, D)[source]¶

Calculates loss coefficient, K, for a given section of pipe at a specified friction factor.

\[K = fL/D\]

Parameters:	f : float friction factor of pipe, [] L : float Length of pipe, [m] D : float Inner diameter of pipe, [m]
Returns:	K : float Loss coefficient, []

Notes

For fittings with a specified L/D ratio, use D = 1 and set L to specified L/D ratio.

Examples

>>> K_from_f(f=0.018, L=100., D=.3)
6.0

fluids.core.K_from_L_equiv(L_D, f=0.015)[source]¶

Calculates loss coefficient, for a given equivalent length (L/D).

\[K = f \frac{L}{D}\]

Parameters:	L_D : float Length over diameter, [] f : float, optional Darcy friction factor, [-]
Returns:	K : float Loss coefficient, []

Notes

Almost identical to K_from_f, but with a default friction factor for fully turbulent flow in steel pipes.

Examples

>>> K_from_L_equiv(240.)
3.5999999999999996

fluids.core.dP_from_K(K, rho, V)[source]¶

Calculates pressure drop, for a given loss coefficient, at a specified density and velocity.

\[dP = 0.5K\rho V^2\]

Parameters:	K : float Loss coefficient, [] rho : float Density of fluid, [kg/m^3] V : float Velocity of fluid in pipe, [m/s]
Returns:	dP : float Pressure drop, [Pa]

Notes

Loss ciefficient K is usually the sum of several factors, including the friction factor.

Examples

>>> dP_from_K(K=10, rho=1000, V=3)
45000.0

fluids.core.head_from_K(K, V)[source]¶

Calculates head loss, for a given loss coefficient, at a specified velocity.

\[\text{head} = \frac{K V^2}{2g}\]

Parameters:	K : float Loss coefficient, [] V : float Velocity of fluid in pipe, [m/s]
Returns:	head : float Head loss, [m]

Notes

Loss ciefficient K is usually the sum of several factors, including the friction factor.

Examples

>>> head_from_K(K=10, V=1.5)
1.1471807396001694

fluids.core.head_from_P(P, rho)[source]¶

Calculates head for a fluid of specified density at specified pressure.

\[\text{head} = {P\over{\rho g}}\]

Parameters:	P : float Pressure fluid in pipe, [Pa] rho : float Density of fluid, [kg/m^3]
Returns:	head : float Head, [m]

Notes

By definition. Head varies with location, inversely propertional to the increase in gravitational constant.

Examples

>>> head_from_P(P=1E5, rho=1000.)
10.197162129779283

fluids.core.P_from_head(head, rho)[source]¶

Calculates head for a fluid of specified density at specified pressure.

\[P = \rho g \cdot \text{head}\]

Parameters:	head : float Head, [m] rho : float Density of fluid, [kg/m^3]
Returns:	P : float Pressure fluid in pipe, [Pa]

Examples

>>> P_from_head(head=5., rho=800.)
39226.6

fluids.filters module¶

Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fluids.filters.round_edge_screen(alpha, Re, angle=0)[source]¶

Returns the loss coefficient for a round edged wire screen or bar screen, as shown in [R272]. Angle of inclination may be specified as well.

Parameters:	alpha : float Fraction of screen open to flow [-] Re : float Reynolds number of flow through screen with D = space between rods, [] angle : float, optional Angle of inclination, with 0 being straight and 90 being parallel to flow [degrees]
Returns:	K : float Loss coefficient [-]

Notes

Linear interpolation between a table of values. Re should be > 20. alpha should be between 0.05 and 0.8. Angle may be no more than 85 degress.

References

[R272]

(1, 2) Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> round_edge_screen(0.5, 100)
2.0999999999999996
>>> round_edge_screen(0.5, 100, 45)
1.05
>>> round_edge_screen(0.5, 100, 85)
0.18899999999999997

fluids.filters.round_edge_open_mesh(alpha, subtype='diamond pattern wire', angle=0)[source]¶

Returns the loss coefficient for a round edged open net/screen made of one of the following patterns, according to [R273]:

‘round bar screen’:

\[K = 0.95(1-\alpha) + 0.2(1-\alpha)^2\]

‘diamond pattern wire’:

\[K = 0.67(1-\alpha) + 1.3(1-\alpha)^2\]

‘knotted net’:

\[K = 0.70(1-\alpha) + 4.9(1-\alpha)^2\]

‘knotless net’:

\[K = 0.72(1-\alpha) + 2.1(1-\alpha)^2\]

Parameters:	alpha : float Fraction of net/screen open to flow [-] subtype : str One of ‘round bar screen’, ‘diamond pattern wire’, ‘knotted net’ or ‘knotless net’. angle : float, optional Angle of inclination, with 0 being straight and 90 being parallel to flow [degrees]
Returns:	K : float Loss coefficient [-]

Notes

alpha should be between 0.85 and 1 for these correlations. Flow should be turbulent, with Re > 500. Angle may be no more than 85 degress.

References

[R273]

(1, 2) Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> [round_edge_open_mesh(0.88, i) for i in ['round bar screen',
... 'diamond pattern wire', 'knotted net', 'knotless net']]
[0.11687999999999998, 0.09912, 0.15455999999999998, 0.11664]
>>> round_edge_open_mesh(0.96, angle=33.)
0.02031327712601458

fluids.filters.square_edge_screen(alpha)[source]¶

Returns the loss coefficient for a square wire screen or square bar screen or perforated plate with squared edges, as shown in [R274].

Parameters:	alpha : float Fraction of screen open to flow [-]
Returns:	K : float Loss coefficient [-]

Notes

Linear interpolation between a table of values.

References

[R274]

(1, 2) Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> square_edge_screen(0.99)
0.008000000000000007

fluids.filters.square_edge_grill(alpha=None, l=None, Dh=None, fd=None)[source]¶

Returns the loss coefficient for a square grill or square bar screen or perforated plate with squared edges of thickness l, as shown in [R275].

for Dh < l < 50D

\[K = \frac{0.5(1-\alpha) + (1-\alpha^2)}{\alpha^2}\]

else:

\[K = \frac{0.5(1-\alpha) + (1-\alpha^2) + f{l}/D}{\alpha^2}\]

Parameters:	alpha : float Fraction of grill open to flow [-] l : float Thickness of the grill or plate [m] Dh : float Hydraulic diameter of gap in grill, [m] fd : float Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

If l, Dh, or fd is not provided, the first expression is used instead. The alteration of the expression to include friction factor is there if the grill is long enough to have considerable friction along the surface of the grill.

References

[R275]

(1, 2) Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> square_edge_grill(.45)
5.296296296296296
>>> square_edge_grill(.45, l=.15, Dh=.002, fd=.0185)
12.148148148148147

fluids.filters.round_edge_grill(alpha=None, l=None, Dh=None, fd=None)[source]¶

Returns the loss coefficient for a rounded square grill or square bar screen or perforated plate with rounded edges of thickness l, as shown in [R276].

for Dh < l < 50D

\[K = lookup(alpha)\]

else:

\[K = lookup(alpha) + \frac{fl}{\alpha^2D}\]

Parameters:	alpha : float Fraction of grill open to flow [-] l : float, optional Thickness of the grill or plate [m] Dh : float, optional Hydraulic diameter of gap in grill, [m] fd : float, optional Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

If l, Dh, or fd is not provided, the first expression is used instead. The alteration of the expression to include friction factor is there if the grill is long enough to have considerable friction along the surface of the grill. alpha must be between 0.3 and 0.7.

References

[R276]

(1, 2) Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> round_edge_grill(.45)
0.8
>>> round_edge_grill(.45, l=.15, Dh=.002, fd=.0185)
2.1875

fluids.fittings module¶

Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fluids.fittings.contraction_sharp(Di1, Di2)[source]¶

Returns loss coefficient for any sharp edged pipe contraction as shown in [R277].

\[K = 0.0696(1-\beta^5)\lambda^2 + (\lambda-1)^2\]\[\lambda = 1 + 0.622(1-0.215\beta^2 - 0.785\beta^5)\]\[\beta = d_2/d_1\]

Parameters:	Di1 : float Inside diameter of original pipe, [m] Di2 : float Inside diameter of following pipe, [m]
Returns:	K : float Loss coefficient [-]

Notes

A value of 0.506 or simply 0.5 is often used.

References

[R277]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> contraction_sharp(Di1=1, Di2=0.4)
0.5301269161591805

fluids.fittings.contraction_round(Di1, Di2, rc)[source]¶

Returns loss coefficient for any round edged pipe contraction as shown in [R278].

\[K = 0.0696\left(1 - 0.569\frac{r}{d_2}\right)\left(1-\sqrt{\frac{r} {d_2}}\beta\right)(1-\beta^5)\lambda^2 + (\lambda-1)^2\]\[\lambda = 1 + 0.622\left(1 - 0.30\sqrt{\frac{r}{d_2}} - 0.70\frac{r}{d_2}\right)^4 (1-0.215\beta^2-0.785\beta^5)\]\[\beta = d_2/d_1\]

Parameters:	Di1 : float Inside diameter of original pipe, [m] Di2 : float Inside diameter of following pipe, [m] rc : float Radius of curvatuce of the contraction, [m]
Returns:	K : float Loss coefficient [-]

Notes

Rounding radius larger than 0.14Di2 prevents flow separation from the wall. Further increase in rounding radius continues to reduce loss coefficient.

References

[R278]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> contraction_round(Di1=1, Di2=0.4, rc=0.04)
0.1783332490866574

fluids.fittings.contraction_conical(Di1, Di2, l=None, angle=None, fd=None)[source]¶

Returns loss coefficient for any conical pipe contraction as shown in [R279].

\[K = 0.0696[1+C_B(\sin(\alpha/2)-1)](1-\beta^5)\lambda^2 + (\lambda-1)^2\]\[\lambda = 1 + 0.622(\alpha/180)^{0.8}(1-0.215\beta^2-0.785\beta^5)\]\[\beta = d_2/d_1\]

Parameters:	Di1 : float Inside diameter of original pipe, [m] Di2 : float Inside diameter of following pipe, [m] l : float Length of the contraction, optional [m] angle : float Angle of contraction, optional [degrees] fd : float Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

Cheap and has substantial impact on pressure drop.

References

[R279]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> contraction_conical(Di1=0.1, Di2=0.04, l=0.04, fd=0.0185)
0.15779041548350314

fluids.fittings.contraction_beveled(Di1, Di2, l=None, angle=None)[source]¶

Returns loss coefficient for any sharp beveled pipe contraction as shown in [R280].

\[K = 0.0696[1+C_B(\sin(\alpha/2)-1)](1-\beta^5)\lambda^2 + (\lambda-1)^2\]\[\lambda = 1 + 0.622\left[1+C_B\left(\left(\frac{\alpha}{180} \right)^{0.8}-1\right)\right](1-0.215\beta^2-0.785\beta^5)\]\[C_B = \frac{l}{d_2}\frac{2\beta\tan(\alpha/2)}{1-\beta}\]\[\beta = d_2/d_1\]

Parameters:	Di1 : float Inside diameter of original pipe, [m] Di2 : float Inside diameter of following pipe, [m] l : float Length of the bevel along the pipe axis ,[m] angle : float Angle of bevel, [degrees]
Returns:	K : float Loss coefficient [-]

References

[R280]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> contraction_beveled(Di1=0.5, Di2=0.1, l=.7*.1, angle=120)
0.40946469413070485

fluids.fittings.diffuser_sharp(Di1, Di2)[source]¶

Returns loss coefficient for any sudded pipe diameter expansion as shown in [R281] and in other sources.

\[K_1 = (1-\beta^2)^2\]

Parameters:	Di1 : float Inside diameter of original pipe (smaller), [m] Di2 : float Inside diameter of following pipe (larger), [m]
Returns:	K : float Loss coefficient [-]

Notes

Highly accurate.

References

[R281]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> diffuser_sharp(Di1=.5, Di2=1)
0.5625

fluids.fittings.diffuser_conical(Di1, Di2, l=None, angle=None, fd=None)[source]¶

Returns loss coefficient for any conical pipe expansion as shown in [R282]. Five different formulas are used, depending on the angle and the ratio of diameters.

For 0 to 20 degrees, all aspect ratios:

\[K_1 = 8.30[\tan(\alpha/2)]^{1.75}(1-\beta^2)^2 + \frac{f(1-\beta^4)}{8\sin(\alpha/2)}\]

For 20 to 60 degrees, beta < 0.5:

\[K_1 = \left\{1.366\sin\left[\frac{2\pi(\alpha-15^\circ)}{180}\right]^{0.5} - 0.170 - 3.28(0.0625-\beta^4)\sqrt{\frac{\alpha-20^\circ}{40^\circ}}\right\} (1-\beta^2)^2 + \frac{f(1-\beta^4)}{8\sin(\alpha/2)}\]

For 20 to 60 degrees, beta >= 0.5:

\[K_1 = \left\{1.366\sin\left[\frac{2\pi(\alpha-15^\circ)}{180}\right]^{0.5} - 0.170 \right\}(1-\beta^2)^2 + \frac{f(1-\beta^4)}{8\sin(\alpha/2)}\]

For 60 to 180 degrees, beta < 0.5:

\[K_1 = \left[1.205 - 3.28(0.0625-\beta^4)-12.8\beta^6\sqrt{\frac {\alpha-60^\circ}{120^\circ}}\right](1-\beta^2)^2\]

For 60 to 180 degrees, beta >= 0.5:

\[K_1 = \left[1.205 - 0.20\sqrt{\frac{\alpha-60^\circ}{120^\circ}} \right](1-\beta^2)^2\]

Parameters:	Di1 : float Inside diameter of original pipe (smaller), [m] Di2 : float Inside diameter of following pipe (larger), [m] l : float Length of the contraction along the pipe axis, optional[m] angle : float Angle of contraction, [degrees] fd : float Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

For angles above 60 degrees, friction factor is not used.

References

[R282]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> diffuser_conical(Di1=.1**0.5, Di2=1, angle=10., fd=0.020)
0.12301652230915454
>>> diffuser_conical(Di1=1/3., Di2=1, angle=50, fd=0.03) # 2
0.8081340270019336
>>> diffuser_conical(Di1=2/3., Di2=1, angle=40, fd=0.03) # 3
0.32533470783539786
>>> diffuser_conical(Di1=1/3., Di2=1, angle=120, fd=0.0185) # #4
0.812308728765127
>>> diffuser_conical(Di1=2/3., Di2=1, angle=120, fd=0.0185) # Last
0.3282650135070033

fluids.fittings.diffuser_conical_staged(Di1, Di2, DEs, ls, fd=None)[source]¶

Returns loss coefficient for any series of staged conical pipe expansions as shown in [R283]. Five different formulas are used, depending on the angle and the ratio of diameters. This function calls diffuser_conical.

Parameters:	Di1 : float Inside diameter of original pipe (smaller), [m] Di2 : float Inside diameter of following pipe (larger), [m] DEs : array Diameters of intermediate sections, [m] ls : array Lengths of the various sections, [m] fd : float Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

Only lengths of sections currently allowed. This could be changed to understand angles also.

Formula doesn’t make much sense, as observed by the example comparing a series of conical sections. Use only for small numbers of segments of highly differing angles.

References

[R283]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> diffuser_conical_staged(Di1=1., Di2=10., DEs=[2,3,4,5,6,7,8,9], ls=[1,1,1,1,1,1,1,1,1], fd=0.01)
1.7681854713484308
>>> diffuser_conical(Di1=1., Di2=10.,l=9, fd=0.01)
0.973137914861591

fluids.fittings.diffuser_curved(Di1, Di2, l)[source]¶

Returns loss coefficient for any curved wall pipe expansion as shown in [R284].

\[K_1 = \phi(1.43-1.3\beta^2)(1-\beta^2)^2\]\[\phi = 1.01 - 0.624\frac{l}{d_1} + 0.30\left(\frac{l}{d_1}\right)^2 - 0.074\left(\frac{l}{d_1}\right)^3 + 0.0070\left(\frac{l}{d_1}\right)^4\]

Parameters:	Di1 : float Inside diameter of original pipe (smaller), [m] Di2 : float Inside diameter of following pipe (larger), [m] l : float Length of the curve along the pipe axis, [m]
Returns:	K : float Loss coefficient [-]

Notes

Beta^2 should be between 0.1 and 0.9. A small mismatch between tabulated values of this function in table 11.3 is observed with the equation presented.

References

[R284]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> diffuser_curved(Di1=.25**0.5, Di2=1., l=2.)
0.2299781250000002

fluids.fittings.diffuser_pipe_reducer(Di1, Di2, l, fd1, fd2=None)[source]¶

Returns loss coefficient for any pipe reducer pipe expansion as shown in [1]. This is an approximate formula.

\[K_f = f_1\frac{0.20l}{d_1} + \frac{f_1(1-\beta)}{8\sin(\alpha/2)} + f_2\frac{0.20l}{d_2}\beta^4\]\[\alpha = 2\tan^{-1}\left(\frac{d_1-d_2}{1.20l}\right)\]

Parameters:	Di1 : float Inside diameter of original pipe (smaller), [m] Di2 : float Inside diameter of following pipe (larger), [m] l : float Length of the pipe reducer along the pipe axis, [m] fd1 : float Darcy friction factor at inlet diameter [-] fd2 : float Darcy friction factor at outlet diameter, optional [-]
Returns:	K : float Loss coefficient [-]

Notes

Industry lack of standardization prevents better formulas from being developed. Add 15% if the reducer is eccentric. Friction factor at outlet will be assumed the same as at inlet if not specified.

Doubt about the validity of this equation is raised.

References

[R285]

Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> diffuser_pipe_reducer(Di1=.5, Di2=.75, l=1.5, fd1=0.07)
0.06873244301714816

fluids.fittings.entrance_sharp()[source]¶

Returns loss coefficient for a sharp entrance to a pipe as shown in [R286].

\[K = 0.57\]

Returns:	K : float Loss coefficient [-]

Notes

Other values used have been 0.5.

References

[R286]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> entrance_sharp()
0.57

fluids.fittings.entrance_distance(d=None, t=None, l=None)[source]¶

Returns loss coefficient for a sharp entrance to a pipe at a distance from the wall of a reservoir, as shown in [R287].

\[K = 1.12 - 22\frac{t}{d} + 216\left(\frac{t}{d}\right)^2 + 80\left(\frac{t}{d}\right)^3\]

Parameters:	Di : float Inside diameter of pipe, [m] t : float Thickness of pipe wall, [m] l : float, optional Length of pipe extending from the wall, [m]
Returns:	K : float Loss coefficient [-]

Notes

Requires that l/d be >= 0.5. Requires that t/d <= 0.05.

References

[R287]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> entrance_distance(d=0.1, t=0.0005)
1.0154100000000004

fluids.fittings.entrance_angled(angle)[source]¶

Returns loss coefficient for a sharp, angled entrance to a pipe flush with the wall of a reservoir, as shown in [R288].

\[K = 0.57 + 0.30\cos(\theta) + 0.20\cos(\theta)^2\]

Parameters:	angle : float Angle of inclination, [degrees]
Returns:	K : float Loss coefficient [-]

Notes

Not reliable for angles under 20 degrees. Loss coefficient is the same for a upward or downward angle.

References

[R288]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> entrance_angled(30)
0.9798076211353316

fluids.fittings.entrance_rounded(Di, rc)[source]¶

Returns loss coefficient for a rounded entrance to a pipe flush with the wall of a reservoir, as shown in [R289].

\[K = 0.0696\left(1 - 0.569\frac{r}{d}\right)\lambda^2 + (\lambda-1)^2\]\[\lambda = 1 + 0.622\left(1 - 0.30\sqrt{\frac{r}{d}} - 0.70\frac{r}{d}\right)^4\]

Parameters:	Di : float Inside diameter of pipe, [m] rd : float Radius of curvatuce of the entrance, [m]
Returns:	K : float Loss coefficient [-]

Notes

Applies for r/D < 1. For generously rounded entrances (r/D ~= 1): K = 0.03

References

[R289]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> entrance_rounded(Di=0.1, rc=0.0235)
0.09839534618360923

fluids.fittings.entrance_beveled(Di, l, angle)[source]¶

Returns loss coefficient for a beveled entrance to a pipe flush with the wall of a reservoir, as shown in [R290].

\[K = 0.0696\left(1 - C_b\frac{l}{d}\right)\lambda^2 + (\lambda-1)^2\]\[\lambda = 1 + 0.622\left[1-1.5C_b\left(\frac{l}{d} \right)^{\frac{1-(l/d)^{1/4}}{2}}\right]\]\[C_b = \left(1 - \frac{\theta}{90}\right)\left(\frac{\theta}{90} \right)^{\frac{1}{l+l/d}}\]

Parameters:	Di : float Inside diameter of pipe, [m] l : float Length of bevel, [m] angle : float Angle of bevel, [degrees]
Returns:	K : float Loss coefficient [-]

Notes

A cheap way of getting a lower pressure drop. Little credible data is available.

References

[R290]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> entrance_beveled(Di=0.1, l=0.003, angle=45)
0.45086864221916984

fluids.fittings.exit_normal()[source]¶

Returns loss coefficient for any exit to a pipe as shown in [R291] and in other sources.

\[K = 1\]

Returns:	K : float Loss coefficient [-]

Notes

It has been found on occasion that K = 2.0 for laminar flow, and ranges from about 1.04 to 1.10 for turbulent flow.

References

[R291]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> exit_normal()
1.0

fluids.fittings.bend_rounded(Di=None, rc=None, angle=None, fd=None, bend_diameters=5)[source]¶

Returns loss coefficient for any rounded bend in a pipe as shown in [R292].

\[K = f\alpha\frac{r}{d} + (0.10 + 2.4f)\sin(\alpha/2) + \frac{6.6f(\sqrt{\sin(\alpha/2)}+\sin(\alpha/2))} {(r/d)^{\frac{4\alpha}{\pi}}}\]

Parameters:	Di : float Inside diameter of pipe, [m] rc : float Radius of curvatuce of the entrance, optional [m] angle : float Angle of bend, [degrees] fd : float Darcy friction factor [-] bend_diameters : float Number of diameters of pipe making up the bend radius [-]
Returns:	K : float Loss coefficient [-]

Notes

When inputting bend diameters, note that manufacturers often specify this as a multiplier of nominal diameter, which is different than actual diameter. Those require that rc be specified.

First term represents surface friction loss; the second, secondary flows; and the third, flow separation. Encompasses the entire range of elbow and pipe bend configurations.

References

[R292]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> [bend_rounded(Di=4.020, rc=4.0*5, angle=i, fd=0.0163) for i in [15, 30, 45, 60, 75, 90]]
[0.07038212630028828, 0.10680196344492195, 0.13858204974134541, 0.16977191374717754, 0.20114941557508642, 0.23248382866658507]
>>> [bend_rounded(Di=34.500, rc=36*10, angle=i, fd=0.0106) for i in [15, 30, 45, 60, 75, 90]]
[0.061075866683922314, 0.10162621862720357, 0.14158887563243763, 0.18225270014527103, 0.22309967045081655, 0.26343782210280947]

fluids.fittings.bend_miter(angle)[source]¶

Returns loss coefficient for any single-joint miter bend in a pipe as shown in [R293].

\[K = 0.42\sin(\alpha/2) + 2.56\sin^3(\alpha/2)\]

Parameters:	angle : float Angle of bend, [degrees]
Returns:	K : float Loss coefficient [-]

Notes

Applies for bends from 0 to 150 degrees. One joint only.

References

[R293]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> [bend_miter(i) for i in [150, 120, 90, 75, 60, 45, 30, 15]]
[2.7128147734758103, 2.0264994448555864, 1.2020815280171306, 0.8332188430731828, 0.5299999999999998, 0.30419633092708653, 0.15308822558050816, 0.06051389308126326]

fluids.fittings.helix(Di=None, rs=None, pitch=None, N=None, fd=None)[source]¶

Returns loss coefficient for any size constant-pitch helix as shown in [R294]. Has applications in immersed coils in tanks.

\[K = N \left[f\frac{\sqrt{(2\pi r)^2 + p^2}}{d} + 0.20 + 4.8 f\right]\]

Parameters:	Di : float Inside diameter of pipe, [m] rs : float Radius of spiral, [m] pitch : float Distance between two subsequent coil centers, [m] N : float Number of coils in the helix [-] fd : float Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

Formulation based on peak secondary flow as in two 180 degree bends per coil. Flow separation ignored. No f, Re, geometry limitations. Source not compared against others.

References

[R294]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> helix(Di=0.01, rs=0.1, pitch=.03, N=10, fd=.0185)
14.525134924495514

fluids.fittings.spiral(Di=None, rmax=None, rmin=None, pitch=None, fd=None)[source]¶

Returns loss coefficient for any size constant-pitch spiral as shown in [R295]. Has applications in immersed coils in tanks.

\[K = \frac{r_{max} - r_{min}}{p} \left[ f\pi\left(\frac{r_{max} +r_{min}}{d}\right) + 0.20 + 4.8f\right] + \frac{13.2f}{(r_{min}/d)^2}\]

Parameters:	Di : float Inside diameter of pipe, [m] rmax : float Radius of spiral at extremity, [m] rmax : float Radius of spiral at end near center, [m] pitch : float Distance between two subsequent coil centers, [m] fd : float Darcy friction factor [-]
Returns:	K : float Loss coefficient [-]

Notes

Source not compared against others.

References

[R295]

(1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.

Examples

>>> spiral(Di=0.01, rmax=.1, rmin=.02, pitch=.01, fd=0.0185)
7.950918552775473

fluids.fittings.Darby3K(NPS=None, Re=None, name=None, K1=None, Ki=None, Kd=None)[source]¶

Returns loss coefficient for any various fittings, depending on the name input. Alternatively, the Darby constants K1, Ki and Kd may be provided and used instead. Source of data is [R296]. Reviews of this model are favorable.

\[K_f = \frac{K_1}{Re} + K_i\left(1 + \frac{K_d}{D_{\text{NPS}}^{0.3}}\right)\]

Parameters:	NPS : float Nominal diameter of the pipe, [in] Re : float Reynolds number, [-] name : str String from Darby dict representing a fitting K1 : float K1 parameter of Darby model, optional [-] Ki : float Ki parameter of Darby model, optional [-] Kd : float Kd parameter of Darby model, optional [in]
Returns:	K : float Loss coefficient [-]

Notes

Also described in Albright’s Handbook and Ludwig’s Applied Process Design. Relatively uncommon to see it used.

The possibility of combining these methods with those above are attractive.

References

[R296]

(1, 2) Silverberg, Peter, and Ron Darby. “Correlate Pressure Drops through Fittings: Three Constants Accurately Calculate Flow through Elbows, Valves and Tees.” Chemical Engineering 106, no. 7 (July 1999): 101.

[R297]

Silverberg, Peter. “Correlate Pressure Drops Through Fittings.” Chemical Engineering 108, no. 4 (April 2001): 127,129-130.

Examples

>>> Darby3K(NPS=2., Re=10000., name='Valve, Angle valve, 45°, full line size, β = 1')
1.1572523963562353
>>> Darby3K(NPS=12., Re=10000., name='Valve, Angle valve, 45°, full line size, β = 1')
0.819510280626355
>>> Darby3K(NPS=12., Re=10000., K1=950,  Ki=0.25,  Kd=4)
0.819510280626355

fluids.fittings.Hooper2K(Di=None, Re=None, name=None, K1=None, Kinfty=None)[source]¶

Returns loss coefficient for any various fittings, depending on the name input. Alternatively, the Hooper constants K1, Kinfty may be provided and used instead. Source of data is [R298]. Reviews of this model are favorable less favorable than the Darby method but superior to the constant-K method.

\[K = \frac{K_1}{Re} + K_\infty\left(1 + \frac{1}{ID_{in}}\right)\]

Parameters:	Di : float Actual inside diameter of the pipe, [in] Re : float Reynolds number, [-] name : str String from Hooper dict representing a fitting K1 : float K1 parameter of Hooper model, optional [-] Kinfty : float Kinfty parameter of Hooper model, optional [-]
Returns:	K : float Loss coefficient [-]

Notes

Also described in Ludwig’s Applied Process Design. Relatively uncommon to see it used. No actual example found.

References

[R298]

(1, 2) Hooper, W. B., “The 2-K Method Predicts Head Losses in Pipe Fittings,” Chem. Eng., p. 97, Aug. 24 (1981).

[R299]

Hooper, William B. “Calculate Head Loss Caused by Change in Pipe Size.” Chemical Engineering 95, no. 16 (November 7, 1988): 89.

[R300]

Kayode Coker. Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. 4E. Amsterdam ; Boston: Gulf Professional Publishing, 2007.

Examples

>>> Hooper2K(Di=2., Re=10000., name='Valve, Globe, Standard')
6.15
>>> Hooper2K(Di=2.067, Re=500., name='Valve, Check, Tilting-disc')
2.7418964683115625

fluids.fittings.Kv_to_Cv(Kv)[source]¶

Convert valve flow coefficient from imperial to common metric units.

\[C_v = 1.1560992283540599 K_v\]

Parameters:	Kv : float Valve flow coefficient, [1 m^3 cold water/hour at dP = 1 bar]
Returns:	Cv : float Valve flow coefficient, [1 gpm water at 1.0 psi dP]

Notes

Kv = 0.865 Cv is in the IEC standard 60534-2-1. It has also been said that Cv = 1.17Kv; this is wrong by current standards.

References

[R301]

ISA-75.01.01-2007 (60534-2-1 Mod) Draft

Examples

>>> Kv_to_Cv(2)
2.3121984567081197

fluids.fittings.Cv_to_Kv(Cv)[source]¶

Convert valve flow coefficient from imperial to common metric units.

\[K_v = C_v/1.156\]

Parameters:	Cv : float Valve flow coefficient, [1 gpm water at 1.0 psi dP]
Returns:	Kv : float Valve flow coefficient, [1 m^3 cold water/hour at dP = 1 bar]

Notes

Kv = 0.865 Cv is in the IEC standard 60534-2-1. It has also been said that Cv = 1.17Kv; this is wrong by current standards.

References

[R302]

ISA-75.01.01-2007 (60534-2-1 Mod) Draft

Examples

>>> Cv_to_Kv(2.312)
1.9998283393819036

fluids.fittings.Kv_to_K(Kv, D)[source]¶

Convert valve flow coefficient from common metric units to regular loss coefficients.

\[K = 0.001604 \frac{D^4}{K_v^2}\]

Parameters:	Kv : float Valve flow coefficient, [1 m^3 cold water/hour at dP = 1 bar]
Returns:	K : float Loss coefficient, [-]

References

[R303]

ISA-75.01.01-2007 (60534-2-1 Mod) Draft

Examples

>>> Kv_to_K(2.312, .015)
15.1912580369009

fluids.friction_factor module¶

Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fluids.friction_factor.friction_factor(Re=100000.0, eD=0.0001, Method=None, Darcy=True, AvailableMethods=False)[source]¶

Calculates friction factor. Uses a specified method, or automatically picks one from the dictionary of available methods. 28 methods available, described in the table below. The default is more than sufficient for all applications. Can also be accesed under the name fd.

Parameters:	Re : float Reynolds number, [-] eD : float Relative roughness of the wall, []
Returns:	f : float Friction factor, [-] methods : list, only returned if AvailableMethods == True List of methods which claim to be valid for the range of Re and eD given
Other Parameters:
	Method : string, optional A string of the function name to use Darcy : bool, optional If False, will return fanning friction factor, 1/4 of the Darcy value AvailableMethods : bool, optional If True, function will consider which methods claim to be valid for the range of Re and eD given

Notes

Nice name	Re min	Re max	Re Default	\(\epsilon/D\) Min	\(\epsilon/D\) Max	\(\epsilon/D\) Default
Rao Kumar 2007	None	None	None	None	None	None
Eck 1973	None	None	None	None	None	None
Jain 1976	5000	1.0E+7	None	4.0E-5	0.05	None
Avci Karagoz 2009	None	None	None	None	None	None
Swamee Jain 1976	5000	1.0E+8	None	1.0E-6	0.05	None
Churchill 1977	None	None	None	None	None	None
Brkic 2011 1	None	None	None	None	None	None
Chen 1979	4000	4.0E+8	None	1.0E-7	0.05	None
Round 1980	4000	4.0E+8	None	0	0.05	None
Papaevangelo 2010	10000	1.0E+7	None	1.0E-5	0.001	None
Fang 2011	3000	1.0E+8	None	0	0.05	None
Shacham 1980	4000	4.0E+8	None	None	None	None
Barr 1981	None	None	None	None	None	None
Churchill 1973	None	None	None	None	None	None
Moody	4000	1.0E+8	None	0	1	None
Zigrang Sylvester 1	4000	1.0E+8	None	4.0E-5	0.05	None
Zigrang Sylvester 2	4000	1.0E+8	None	4.0E-5	0.05	None
Buzzelli 2008	None	None	None	None	None	None
Haaland	4000	1.0E+8	None	1.0E-6	0.05	None
Serghides 1	None	None	None	None	None	None
Serghides 2	None	None	None	None	None	None
Tsal 1989	4000	1.0E+8	None	0	0.05	None
Alshul 1952	None	None	None	None	None	None
Wood 1966	4000	5.0E+7	None	1.0E-5	0.04	None
Manadilli 1997	5245	1.0E+8	None	0	0.05	None
Brkic 2011 2	None	None	None	None	None	None
Romeo 2002	3000	1.5E+8	None	0	0.05	None
Sonnad Goudar 2006	4000	1.0E+8	None	1.0E-6	0.05	None

Examples

>>> friction_factor(Re=1E5, eD=1E-4)
0.018513948401365277