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]

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

R80

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

R81

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

R82

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

R83

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

R84

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

R85(1,2)

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

R86

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

Examples

Example 4 of [R85], 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

R87

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

R88

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

R89

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

R90

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

R91

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

R92

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

R93

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

R94

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

R95

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

R96

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

R97

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

R98

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

R99

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

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

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

References

R100

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

R101

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

R102

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

R103

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

R104

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

R105

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

R106

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

R107

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

R108

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

R109

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

R110

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

R111

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

R112

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]

Returns

Mo : float

Morton number, [-]

Notes

Used in modeling bubbles in liquid.

References

R113

Kunes, Josef. Dimensionless Physical Quantities in Science and Engineering. Elsevier, 2012.

R114

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

Returns

Fr : float

Froude number, [-]

Notes

Many alternate definitions including density ratios have been used.

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

References

R115

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

R116

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]

Returns

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

R117

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]

Returns

St : float

Strouhal number, [-]

Notes

Sometimes abbreviated to S or Sr.

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

References

R118

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

R119

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

R120

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

R121

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

R122

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

R122

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

R124

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

R125

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

R126

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

R127

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

R128

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

R129

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

R130

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

R131

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

R132

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]

Returns

Stk : float

Stokes numer, [-]

Notes

Used in droplet impaction or collection studies.

References

R133

Rhodes, Martin J. Introduction to Particle Technology. Wiley, 2013.

R134

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]

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

R135

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

R136

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

R137

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

R138

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

R139

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.

R140

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

R141

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.

R142

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 [R146], though not named.

References

R143

Winterton, Richard H.S. BOILING NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.b.boiling_number

R144

Collier, John G., and John R. Thome. Convective Boiling and Condensation. 3rd edition. Clarendon Press, 1996.

R145

Stephan, Karl. Heat Transfer in Condensation and Boiling. Translated by C. V. Green.. 1992 edition. Berlin; New York: Springer, 2013.

R146(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 [R147] according to [R149].

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

References

R147(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.

R148

Kandlikar, Satish G. Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier, 2006.

R149(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

R151

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

R152

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

R153

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 [R155].

References

R154

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.

R155(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, [-]

Returns

Hg : float

Hagen number, [-]

Notes

Introduced in [R156]; further use of it is mostly of the correlations introduced in [R156].

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

R156(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.

R157

Shah, Ramesh K., and Dusan P. Sekulic. Fundamentals of Heat Exchanger Design. 1st edition. Hoboken, NJ: Wiley, 2002.

R158(1,2)

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

Examples

Example from [R158]:

>>> 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]

Returns

alpha : float

Thermal diffusivity, [m^2/s]

References

R159

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

R160

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

R161

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)
348.9820953185441
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

R162

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

R163

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.

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

R164

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 [R165]. 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

R165(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 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
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 coefficient 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

R166

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