Dimentionless 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
[R72] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R73] 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
[R74] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R75] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. [R76] 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
[R77] (1, 2) Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R78] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. Examples
Example 4 of [R77], 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
[R79] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R80] 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
[R81] 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
[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. 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
[R84] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R85] 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
[R86] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R87] 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
[R88] 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
[R89] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R90] 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
[R91] 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
\[ \begin{align}\begin{aligned}Gz = \frac{\text{Time for radial heat diffusion in a fluid by conduction}} {\text{Time taken by fluid to reach distance x}}\\Gz = \frac{D}{x}RePr\end{aligned}\end{align} \]An error is raised if none of the required input sets are provided.
References
[R92] 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
[R93] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R94] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. [R95] 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
[R96] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R97] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. [R98] 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
[R99] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R100] 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
[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. 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
[R103] 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
[R104] 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
[R105] Kunes, Josef. Dimensionless Physical Quantities in Science and Engineering. Elsevier, 2012. [R106] 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
[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
>>> 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
[R109] 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
[R110] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R111] 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
[R112] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R113] 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
[R114] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R114] 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
[R116] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R117] 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
[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
>>> 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
[R120] 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
[R121] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011. [R122] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. Examples
>>> Jakob(4000., 2E6, 10.) 0.02
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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
[R123] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R124] 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
[R125] Rhodes, Martin J. Introduction to Particle Technology. Wiley, 2013. [R126] 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
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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
[R127] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R128] 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
[R129] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R130] 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
[R131] 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. [R132] Bejan, Adrian. Convection Heat Transfer. 4E. Hoboken, New Jersey: Wiley, 2013. Examples
>>> Bejan_L(1E4, 1, 1E-3, 1E-6) 10000000000000.0
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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
[R133] 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. [R134] Bejan, Adrian. Convection Heat Transfer. 4E. Hoboken, New Jersey: Wiley, 2013. Examples
>>> Bejan_p(1E4, 1, 1E-3, 1E-6) 10000000000000.0
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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 [R138], though not named.
References
[R135] Winterton, Richard H.S. BOILING NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.b.boiling_number [R136] Collier, John G., and John R. Thome. Convective Boiling and Condensation. 3rd edition. Clarendon Press, 1996. [R137] Stephan, Karl. Heat Transfer in Condensation and Boiling. Translated by C. V. Green.. 1992 edition. Berlin; New York: Springer, 2013. [R138] (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
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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 [R139] according to [R141].
\[\text{Co} = \frac{\frac{\text{surface tension force}} {\text{buoyancy force}}}{\text{Channel area}}\]References
[R139] (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. [R140] Kandlikar, Satish G. Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier, 2006. [R141] (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
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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
[R143] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R144] 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
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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
[R145] 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
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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 [R147].
References
[R146] 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. [R147] (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
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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 [R148]; further use of it is mostly of the correlations introduced in [R148].
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
[R148] (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. [R149] Shah, Ramesh K., and Dusan P. Sekulic. Fundamentals of Heat Exchanger Design. 1st edition. Hoboken, NJ: Wiley, 2002. [R150] (1, 2) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010. Examples
Example from [R150]:
>>> 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
[R151] 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
[R152] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R153] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. Examples
>>> c_ideal_gas(T=303, k=1.4, MW=28.96) 348.9820361755092
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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
[R154] Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007. [R155] 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
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fluids.core.
nu_mu_converter
(rho, mu=None, nu=None)[source]¶ Calculates either kinematic or dynamic viscosity, depending on inputs. Used when one type of viscosity is known as well as density, to obtain the other type. Raises an error if both types of viscosity or neither type of viscosity is provided.
\[ \begin{align}\begin{aligned}\nu = \frac{\mu}{\rho}\\\mu = \nu\rho\end{aligned}\end{align} \]Parameters: rho : float
Density, [kg/m^3]
mu : float, optional
Dynamic viscosity, [Pa*s]
nu : float, optional
Kinematic viscosity, [m^2/s]
Returns: mu or nu : float
Dynamic viscosity, Pa*s or Kinematic viscosity, m^2/s
References
[R156] 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
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fluids.core.
gravity
(latitude, H)[source]¶ Calculates local acceleration due to gravity g according to [R157]. 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
[R157] (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
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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
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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
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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
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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
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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
[R158] 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