# Dimensionless 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] 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

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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
 [3] 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] 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

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

Examples

Example 4 of [1], 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] 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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Sh : float Sherwood number, [-]

Notes

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

References

 [1] 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 [] Ra : float Rayleigh number []

Notes

Used in free convection problems only.

References

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

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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Pe : float Peclet number (mass) []

Notes

$Pe = \frac{\text{Advective transport rate}}{\text{Diffusive transport rate}}$

References

 [1] 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] 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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Fo : float Fourier number (mass) []

Notes

$Fo = \frac{\text{Diffusive transport rate}}{\text{Storage rate}}$

References

 [1] 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] 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

 [1] 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] 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

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

Notes

Used in bubble calculations.

$We = \frac{\text{inertial force}}{\text{surface tension force}}$

References

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

Notes

Used in compressible flow calculations.

$Ma = \frac{\text{fluid velocity}}{\text{sonic velocity}}$

References

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Kn : float Knudsen number []

Notes

Used in mass transfer calculations.

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

References

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Bo : float Bond number []

References

 [1] 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 [] 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

 [1] 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.Morton(rhol, rhog, mul, sigma, g=9.80665)[source]

Calculates Morton number or Mo for a liquid and vapor with the specified properties, under the influence of gravitational force g.

$Mo = \frac{g \mu_l^4(\rho_l - \rho_g)}{\rho_l^2 \sigma^3}$
Parameters: rhol : float Density of liquid phase, [kg/m^3] rhog : float Density of gas phase, [kg/m^3] mul : float Viscosity of liquid phase, [Pa*s] sigma : float Surface tension between liquid-gas phase, [N/m] g : float, optional Acceleration due to gravity, [m/s^2] Mo : float Morton number, [-]

Notes

Used in modeling bubbles in liquid.

References

 [1] Kunes, Josef. Dimensionless Physical Quantities in Science and Engineering. Elsevier, 2012.
 [2] Yan, Xiaokang, Kaixin Zheng, Yan Jia, Zhenyong Miao, Lijun Wang, Yijun Cao, and Jiongtian Liu. “Drag Coefficient Prediction of a Single Bubble Rising in Liquids.” Industrial & Engineering Chemistry Research, April 2, 2018. https://doi.org/10.1021/acs.iecr.7b04743.

Examples

>>> Morton(1077.0, 76.5, 4.27E-3, 0.023)
2.311183104430743e-07
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 Fr : float Froude number, [-]

Notes

Many alternate definitions including density ratios have been used.

$Fr = \frac{\text{Inertial Force}}{\text{Gravity Force}}$

References

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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.Froude_densimetric(V, L, rho1, rho2, heavy=True, g=9.80665)[source]

Calculates the densimetric Froude number $$Fr_{den}$$ for velocity V geometric length L, heavier fluid density rho1, and lighter fluid density rho2. If desired, gravity can be specified as well. Depending on the application, this dimensionless number may be defined with the heavy phase or the light phase density in the numerator of the square root. For some applications, both need to be calculated. The default is to calculate with the heavy liquid ensity on top; set heavy to False to reverse this.

$Fr = \frac{V}{\sqrt{gL}} \sqrt{\frac{\rho_\text{(1 or 2)}} {\rho_1 - \rho_2}}$
Parameters: V : float Velocity of the specified phase, [m/s] L : float Characteristic length, no typical definition [m] rho1 : float Density of the heavier phase, [kg/m^3] rho2 : float Density of the lighter phase, [kg/m^3] heavy : bool, optional Whether or not the density used in the numerator is the heavy phase or the light phase, [-] g : float, optional Acceleration due to gravity, [m/s^2] Fr_den : float Densimetric Froude number, [-]

Notes

Many alternate definitions including density ratios have been used.

$Fr = \frac{\text{Inertial Force}}{\text{Gravity Force}}$

Where the gravity force is reduced by the relative densities of one fluid in another.

Note that an Exception will be raised if rho1 > rho2, as the square root becomes negative.

References

 [1] Hall, A, G Stobie, and R Steven. “Further Evaluation of the Performance of Horizontally Installed Orifice Plate and Cone Differential Pressure Meters with Wet Gas Flows.” In International SouthEast Asia Hydrocarbon Flow Measurement Workshop, KualaLumpur, Malaysia, 2008.

Examples

>>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81)
0.4134543386272418
>>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81, heavy=False)
0.016013017679205096
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] St : float Strouhal number, [-]

Notes

Sometimes abbreviated to S or Sr.

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

References

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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] St : float Stanton number []

Notes

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

References

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

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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Ec : float Eckert number []

Notes

Used in certain heat transfer calculations. Fairly rare.

$Ec = \frac{\text{Kinetic energy} }{ \text{Enthalpy difference}}$

References

 [1] 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] Ja : float Jakob number []

Notes

Used in boiling heat transfer analysis. Fairly rare.

$Ja = \frac{\Delta \text{Sensible heat}}{\Delta \text{Latent heat}}$

References

 [1] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
 [2] 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] Po : float Power number []

Notes

Used in mixing calculations.

$Po = \frac{\text{Power}}{\text{Rotational inertia}}$

References

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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.Stokes_number(V, Dp, D, rhop, mu)[source]

Calculates Stokes Number for a given characteristic velocity V, particle diameter Dp, characteristic diameter D, particle density rhop, and fluid viscosity mu.

$\text{Stk} = \frac{\rho_p V D_p^2}{18\mu_f D}$
Parameters: V : float Characteristic velocity (often superficial), [m/s] Dp : float Particle diameter, [m] D : float Characteristic diameter (ex demister wire diameter or cyclone diameter), [m] rhop : float Particle density, [kg/m^3] mu : float Fluid viscosity, [Pa*s] Stk : float Stokes numer, [-]

Notes

Used in droplet impaction or collection studies.

References

 [1] Rhodes, Martin J. Introduction to Particle Technology. Wiley, 2013.
 [2] Al-Dughaither, Abdullah S., Ahmed A. Ibrahim, and Waheed A. Al-Masry. “Investigating Droplet Separation Efficiency in Wire-Mesh Mist Eliminators in Bubble Column.” Journal of Saudi Chemical Society 14, no. 4 (October 1, 2010): 331-39. https://doi.org/10.1016/j.jscs.2010.04.001.

Examples

>>> Stokes_number(V=0.9, Dp=1E-5, D=1E-3, rhop=1000, mu=1E-5)
0.5
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] 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

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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] Be_L : float Bejan number with respect to length []

Notes

Termed a dimensionless number by someone in 1988.

References

 [1] 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.
 [2] 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] Be_p : float Bejan number with respect to pore characteristics []

Notes

Termed a dimensionless number by someone in 1988.

References

 [1] 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.
 [2] 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] 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 [4], though not named.

References

 [1] Winterton, Richard H.S. BOILING NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.b.boiling_number
 [2] Collier, John G., and John R. Thome. Convective Boiling and Condensation. 3rd edition. Clarendon Press, 1996.
 [3] Stephan, Karl. Heat Transfer in Condensation and Boiling. Translated by C. V. Green.. 1992 edition. Berlin; New York: Springer, 2013.
 [4] (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] Co : float Confinement number [-]

Notes

Used in two-phase pressure drop and heat transfer correlations. First used in [1] according to [3].

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

References

 [1] (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.
 [2] Kandlikar, Satish G. Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier, 2006.
 [3] (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] Ar : float Archimedes number []

Notes

Used in fluid-particle interaction calculations.

$Ar = \frac{\text{Gravitational force}}{\text{Viscous force}}$

References

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

 [1] 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] 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 [2].

References

 [1] 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.
 [2] (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.Hagen(Re, fd)[source]

Calculates Hagen number, Hg, for a fluid with the given Reynolds number and friction factor.

$\text{Hg} = \frac{f_d}{2} Re^2 = \frac{1}{\rho} \frac{\Delta P}{\Delta z} \frac{D^3}{\nu^2} = \frac{\rho\Delta P D^3}{\mu^2 \Delta z}$
Parameters: Re : float Reynolds number [-] fd : float, optional Darcy friction factor, [-] Hg : float Hagen number, [-]

Notes

Introduced in [1]; further use of it is mostly of the correlations introduced in [1].

Notable for use use in correlations, because it does not have any dependence on velocity.

This expression is useful when designing backwards with a pressure drop spec already known.

References

 [1] (1, 2, 3) Martin, Holger. “The Generalized Lévêque Equation and Its Practical Use for the Prediction of Heat and Mass Transfer Rates from Pressure Drop.” Chemical Engineering Science, Jean-Claude Charpentier Festschrift Issue, 57, no. 16 (August 1, 2002): 3217-23. https://doi.org/10.1016/S0009-2509(02)00194-X.
 [2] Shah, Ramesh K., and Dusan P. Sekulic. Fundamentals of Heat Exchanger Design. 1st edition. Hoboken, NJ: Wiley, 2002.
 [3] (1, 2) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

Examples

Example from [3]:

>>> Hagen(Re=2610, fd=1.935235)
6591507.17175
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] alpha : float Thermal diffusivity, [m^2/s]

References

 [1] 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] 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

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] eD : float Relative Roughness, [-]

References

 [1] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
 [2] 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] mu or nu : float Dynamic viscosity, Pa*s or Kinematic viscosity, m^2/s

References

 [1] 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 [1]. 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] g : float Acceleration due to gravity, [m/s^2]

Notes

Better models, such as EGM2008 exist.

References

 [1] (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] 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, [-] 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, [-] 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, [] 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] dP : float Pressure drop, [Pa]

Notes

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

Examples

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

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] head : float Head loss, [m]

Notes

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

Examples

1.1471807396001694

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] head : float Head, [m]

Notes

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

Examples

10.000000000000002

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] P : float Pressure fluid in pipe, [Pa]

Examples

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] Bo : float Bond number []

References

 [1] 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