Dimentionless numbers (fluids.core)

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.

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

Inputs either of any of the following sets:

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

V : float

Velocity [m/s]

D : float

Diameter [m]

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

[R141219]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R142219]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

[R143221]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R144221]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
[R145221]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

[R146224](1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R147224]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

Example 4 of [R146224], 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

[R148226]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R149226]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

[R150228]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

[R151229]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R152229]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

[R153231]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R154231]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 capacity 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

[R155233]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R156233]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

[R157235]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 capacity 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

[R158236]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R159236]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Fourier_heat(t=1.5, L=2, rho=1000., Cp=4000., k=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

[R160238]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Fourier_mass(t=1.5, L=2, D=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 distance 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 capacity 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

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

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

References

[R161239]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

[R162240]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R163240]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
[R164240]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

[R165243]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R166243]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
[R167243]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

[R168246]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R169246]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

[R170248]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R171248]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

[R172250]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.Dean(Re, Di, D)[source]

Calculates Dean number, De, for a fluid with the Reynolds number Re, inner diameter Di, and a secondary diameter D. D may be the diameter of curvature, the diameter of a spiral, or some other dimension.

\[\text{De} = \sqrt{\frac{D_i}{D}} \text{Re} = \sqrt{\frac{D_i}{D}} \frac{\rho v D}{\mu}\]
Parameters:

Re : float

Reynolds number []

Di : float

Inner diameter []

D : float

Diameter of curvature or outer spiral or other dimension []

Returns:

De : float

Dean number [-]

Notes

Used in flow in curved geometry.

\[\text{De} = \frac{\sqrt{\text{centripetal forces}\cdot \text{inertial forces}}}{\text{viscous forces}}\]

References

[R173251]Catchpole, John P., and George. Fulford. “DIMENSIONLESS GROUPS.” Industrial & Engineering Chemistry 58, no. 3 (March 1, 1966): 46-60. doi:10.1021/ie50675a012.

Examples

>>> Dean(10000, 0.1, 0.4)
5000.0
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 Froude 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

[R174252]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R175252]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.

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

References

[R176254]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R177254]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

[R178256]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R179256]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

[R180258]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R180258]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

[R182260]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R183260]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

[R184262]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R185262]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

[R186264]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

[R187265]Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
[R188265]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, rotational 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

[R189267]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R190267]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

[R191269]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R192269]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

[R193271]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R194271]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.Bejan_L(dP, L, mu, alpha)[source]

Calculates Bejan number of a length or Be_L for a fluid with the given parameters flowing over a characteristic length L and experiencing a pressure drop dP.

\[Be_L = \frac{\Delta P L^2}{\mu \alpha}\]
Parameters:

dP : float

Pressure drop, [Pa]

L : float

Characteristic length, [m]

mu : float, optional

Dynamic viscosity, [Pa*s]

alpha : float

Thermal diffusivity, [m^2/s]

Returns:

Be_L : float

Bejan number with respect to length []

Notes

Termed a dimensionless number by someone in 1988.

References

[R195273]Awad, M. M. “The Science and the History of the Two Bejan Numbers.” International Journal of Heat and Mass Transfer 94 (March 2016): 101-3. doi:10.1016/j.ijheatmasstransfer.2015.11.073.
[R196273]Bejan, Adrian. Convection Heat Transfer. 4E. Hoboken, New Jersey: Wiley, 2013.

Examples

>>> Bejan_L(1E4, 1, 1E-3, 1E-6)
10000000000000.0
fluids.core.Bejan_p(dP, K, mu, alpha)[source]

Calculates Bejan number of a permeability or Be_p for a fluid with the given parameters and a permeability K experiencing a pressure drop dP.

\[Be_p = \frac{\Delta P K}{\mu \alpha}\]
Parameters:

dP : float

Pressure drop, [Pa]

K : float

Permeability, [m^2]

mu : float, optional

Dynamic viscosity, [Pa*s]

alpha : float

Thermal diffusivity, [m^2/s]

Returns:

Be_p : float

Bejan number with respect to pore characteristics []

Notes

Termed a dimensionless number by someone in 1988.

References

[R197275]Awad, M. M. “The Science and the History of the Two Bejan Numbers.” International Journal of Heat and Mass Transfer 94 (March 2016): 101-3. doi:10.1016/j.ijheatmasstransfer.2015.11.073.
[R198275]Bejan, Adrian. Convection Heat Transfer. 4E. Hoboken, New Jersey: Wiley, 2013.

Examples

>>> Bejan_p(1E4, 1, 1E-3, 1E-6)
10000000000000.0
fluids.core.Boiling(G, q, Hvap)[source]

Calculates Boiling number or Bg using heat flux, two-phase mass flux, and heat of vaporization of the fluid flowing. Used in two-phase heat transfer calculations.

\[\text{Bg} = \frac{q}{G_{tp} \Delta H_{vap}}\]
Parameters:

G : float

Two-phase mass flux in a channel (combined liquid and vapor) [kg/m^2/s]

q : float

Heat flux [W/m^2]

Hvap : float

Heat of vaporization of the fluid [J/kg]

Returns:

Bg : float

Boiling number [-]

Notes

Most often uses the symbol Bo instead of Bg, but this conflicts with Bond number.

\[\text{Bg} = \frac{\text{mass liquid evaporated / area heat transfer surface}}{\text{mass flow rate fluid / flow cross sectional area}}\]

First defined in [R202277], though not named.

References

[R199277]Winterton, Richard H.S. BOILING NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.b.boiling_number
[R200277]Collier, John G., and John R. Thome. Convective Boiling and Condensation. 3rd edition. Clarendon Press, 1996.
[R201277]Stephan, Karl. Heat Transfer in Condensation and Boiling. Translated by C. V. Green.. 1992 edition. Berlin; New York: Springer, 2013.
[R202277](1, 2) W. F. Davidson, P. H. Hardie, C. G. R. Humphreys, A. A. Markson, A. R. Mumford and T. Ravese “Studies of heat transmission through boiler tubing at pressures from 500 to 3300 pounds” Trans. ASME, Vol. 65, 9, February 1943, pp. 553-591.

Examples

>>> Boiling(300, 3000, 800000)
1.25e-05
fluids.core.Confinement(D, rhol, rhog, sigma, g=9.80665)[source]

Calculates Confinement number or Co for a fluid in a channel of diameter D with liquid and gas densities rhol and rhog and surface tension sigma, under the influence of gravitational force g.

\[\text{Co}=\frac{\left[\frac{\sigma}{g(\rho_l-\rho_g)}\right]^{0.5}}{D}\]
Parameters:

D : float

Diameter of channel, [m]

rhol : float

Density of liquid phase, [kg/m^3]

rhog : float

Density of gas phase, [kg/m^3]

sigma : float

Surface tension between liquid-gas phase, [N/m]

g : float, optional

Acceleration due to gravity, [m/s^2]

Returns:

Co : float

Confinement number [-]

Notes

Used in two-phase pressure drop and heat transfer correlations. First used in [R203281] according to [R205281].

\[\text{Co} = \frac{\frac{\text{surface tension force}} {\text{buoyancy force}}}{\text{Channel area}}\]

References

[R203281](1, 2) Cornwell, Keith, and Peter A. Kew. “Boiling in Small Parallel Channels.” In Energy Efficiency in Process Technology, edited by Dr P. A. Pilavachi, 624-638. Springer Netherlands, 1993. doi:10.1007/978-94-011-1454-7_56.
[R204281]Kandlikar, Satish G. Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier, 2006.
[R205281](1, 2) Tran, T. N, M. -C Chyu, M. W Wambsganss, and D. M France. Two-Phase Pressure Drop of Refrigerants during Flow Boiling in Small Channels: An Experimental Investigation and Correlation Development.” International Journal of Multiphase Flow 26, no. 11 (November 1, 2000): 1739-54. doi:10.1016/S0301-9322(99)00119-6.

Examples

>>> Confinement(0.001, 1077, 76.5, 4.27E-3)
0.6596978265315191
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

[R207285]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R208285]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> Archimedes(0.002, 2., 3000, 1E-3)
470.4053872
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

[R209287]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

>>> Ohnesorge(1E-4, 1000., 1E-3, 1E-1)
0.01
fluids.core.Suratman(L, rho, mu, sigma)[source]

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

\[\text{Su} = \frac{\rho\sigma L}{\mu^2}\]
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:

Su : float

Suratman number []

Notes

Also known as Laplace number. Used in two-phase flow, especially the bubbly-slug regime. No confusion regarding the definition of this group has been observed.

\[\text{Su} = \frac{\text{Re}^2}{\text{We}} =\frac{\text{Inertia}\cdot \text{Surface tension} }{\text{(viscous forces)}^2}\]

The oldest reference to this group found by the author is in 1963, from [R211288].

References

[R210288]Sen, Nilava. “Suratman Number in Bubble-to-Slug Flow Pattern Transition under Microgravity.” Acta Astronautica 65, no. 3-4 (August 2009): 423-28. doi:10.1016/j.actaastro.2009.02.013.
[R211288](1, 2) Catchpole, John P., and George. Fulford. “DIMENSIONLESS GROUPS.” Industrial & Engineering Chemistry 58, no. 3 (March 1, 1966): 46-60. doi:10.1021/ie50675a012.

Examples

>>> Suratman(1E-4, 1000., 1E-3, 1E-1)
10000.0
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]

rho : float

Density, [kg/m^3]

Cp : float

Heat capacity, [J/kg/K]

Returns:

alpha : float

Thermal diffusivity, [m^2/s]

References

[R212290]Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.

Examples

>>> thermal_diffusivity(k=0.02, rho=1., Cp=1000.)
2e-05
fluids.core.c_ideal_gas(T, k, MW)[source]

Calculates speed of sound c in an ideal gas at temperature 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

[R213291]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R214291]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> c_ideal_gas(T=303, k=1.4, MW=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

[R215293]Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
[R216293]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> relative_roughness(0.5, 1E-4)
0.0002
fluids.core.nu_mu_converter(rho, mu=None, nu=None)[source]

Calculates either kinematic or dynamic viscosity, depending on inputs. Used when one type of viscosity is known as well as density, to obtain the other type. Raises an error if both types of viscosity or neither type of viscosity is provided.

\[ \begin{align}\begin{aligned}\nu = \frac{\mu}{\rho}\\\mu = \nu\rho\end{aligned}\end{align} \]
Parameters:

rho : float

Density, [kg/m^3]

mu : float, optional

Dynamic viscosity, [Pa*s]

nu : float, optional

Kinematic viscosity, [m^2/s]

Returns:

mu or nu : float

Dynamic viscosity, Pa*s or Kinematic viscosity, m^2/s

References

[R217295]Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.

Examples

>>> nu_mu_converter(998., nu=1.0E-6)
0.000998
fluids.core.gravity(latitude, H)[source]

Calculates local acceleration due to gravity g according to [R218296]. 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]

H : 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

[R218296](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(fd, L, D)[source]

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

\[K = f_dL/D\]
Parameters:

fd : 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(fd=0.018, L=100., D=.3)
6.0
fluids.core.K_from_L_equiv(L_D, fd=0.015)[source]

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

\[K = f_d \frac{L}{D}\]
Parameters:

L_D : float

Length over diameter, []

fd : 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.L_equiv_from_K(K, fd=0.015)[source]

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

\[\frac{L}{D} = \frac{K}{f_d}\]
Parameters:

K : float

Loss coefficient, []

fd : float, optional

Darcy friction factor, [-]

Returns:

L_D : float

Length over diameter, []

Notes

Assumes a default friction factor for fully turbulent flow in steel pipes.

Examples

>>> L_equiv_from_K(3.6)
240.00000000000003
fluids.core.L_from_K(K, D, fd=0.015)[source]

Calculates the length of straight pipe at a specified friction factor required to produce a given loss coefficient K.

\[L = \frac{K D}{f_d}\]
Parameters:

K : float

Loss coefficient, []

D : float

Inner diameter of pipe, [m]

fd : float

friction factor of pipe, []

Returns:

L : float

Length of pipe, [m]

Examples

>>> L_from_K(K=6, D=.3, fd=0.018)
100.0
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, g=9.80665)[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]

g : float, optional

Acceleration due to gravity, [m/s^2]

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, g=9.80665)[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]

g : float, optional

Acceleration due to gravity, [m/s^2]

Returns:

head : float

Head, [m]

Notes

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

Examples

>>> head_from_P(P=98066.5, rho=1000)
10.000000000000002
fluids.core.P_from_head(head, rho, g=9.80665)[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]

g : float, optional

Acceleration due to gravity, [m/s^2]

Returns:

P : float

Pressure fluid in pipe, [Pa]

Examples

>>> P_from_head(head=5., rho=800.)
39226.6
fluids.core.Eotvos(rhol, rhog, sigma, L)

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

[R219297]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