Dimensionless numbers (fluids.core)¶
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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