Dimensionless numbers (fluids.core)¶
This module contains basic fluid mechanics and engineering calculations which have been found useful by the author. The main functionality is calculating dimensionless numbers, interconverting different forms of loss coefficients, and converting temperature units.
For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.
Dimensionless Numbers¶
- 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).
- Parameters
- Returns
- Ar
float
Archimedes number []
- Ar
Notes
Used in fluid-particle interaction calculations.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Archimedes(0.002, 2., 3000, 1E-3) 470.4053872
- fluids.core.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.
- Parameters
- Returns
- Be_L
float
Bejan number with respect to length []
- Be_L
Notes
Termed a dimensionless number by someone in 1988.
References
- 1
Awad, M. M. “The Science and the History of the Two Bejan Numbers.” International Journal of Heat and Mass Transfer 94 (March 2016): 101-3. doi:10.1016/j.ijheatmasstransfer.2015.11.073.
- 2
Bejan, Adrian. Convection Heat Transfer. 4E. Hoboken, New Jersey: Wiley, 2013.
Examples
>>> Bejan_L(1E4, 1, 1E-3, 1E-6) 10000000000000.0
- fluids.core.Bejan_p(dP, K, mu, alpha)[source]¶
Calculates Bejan number of a permeability or Be_p for a fluid with the given parameters and a permeability K experiencing a pressure drop dP.
- Parameters
- Returns
- Be_p
float
Bejan number with respect to pore characteristics []
- Be_p
Notes
Termed a dimensionless number by someone in 1988.
References
- 1
Awad, M. M. “The Science and the History of the Two Bejan Numbers.” International Journal of Heat and Mass Transfer 94 (March 2016): 101-3. doi:10.1016/j.ijheatmasstransfer.2015.11.073.
- 2
Bejan, Adrian. Convection Heat Transfer. 4E. Hoboken, New Jersey: Wiley, 2013.
Examples
>>> Bejan_p(1E4, 1, 1E-3, 1E-6) 10000000000000.0
- fluids.core.Biot(h, L, k)[source]¶
Calculates Biot number Br for heat transfer coefficient h, geometric length L, and thermal conductivity k.
- Parameters
- Returns
- Bi
float
Biot number, [-]
- Bi
Notes
Do not confuse k, the thermal conductivity within the object, with that of the medium h is calculated with!
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Biot(1000., 1.2, 300.) 4.0 >>> Biot(10000., .01, 4000.) 0.025
- fluids.core.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.
- Parameters
- Returns
- Bg
float
Boiling number [-]
- Bg
Notes
Most often uses the symbol Bo instead of Bg, but this conflicts with Bond number.
First defined in [4], though not named.
References
- 1
Winterton, Richard H.S. BOILING NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.b.boiling_number
- 2
Collier, John G., and John R. Thome. Convective Boiling and Condensation. 3rd edition. Clarendon Press, 1996.
- 3
Stephan, Karl. Heat Transfer in Condensation and Boiling. Translated by C. V. Green.. 1992 edition. Berlin; New York: Springer, 2013.
- 4
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.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).
- Parameters
- Returns
- Bo
float
Bond number []
- Bo
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
Examples
>>> Bond(1000., 1.2, .0589, 2) 665187.2339558573
- fluids.core.Capillary(V, mu, sigma)[source]¶
Calculates Capillary number Ca for a characteristic velocity V, viscosity mu, and surface tension sigma.
- Parameters
- Returns
- Ca
float
Capillary number, [-]
- Ca
Notes
Used in porous media calculations and film flow calculations. Surface tension may gas-liquid, or liquid-liquid.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Kundu, Pijush K., Ira M. Cohen, and David R. Dowling. Fluid Mechanics. Academic Press, 2012.
Examples
>>> Capillary(1.2, 0.01, .1) 0.12
- fluids.core.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.
- Parameters
- Returns
- Ca
float
Cavitation number []
- Ca
Notes
Used in determining if a flow through a restriction will cavitate. Sometimes, the multiplication by 2 will be omitted;
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Cavitation(2E5, 1E4, 1000, 10) 3.8
- fluids.core.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.
- Parameters
- Returns
- Co
float
Confinement number [-]
- Co
Notes
Used in two-phase pressure drop and heat transfer correlations. First used in [1] according to [3].
References
- 1
Cornwell, Keith, and Peter A. Kew. “Boiling in Small Parallel Channels.” In Energy Efficiency in Process Technology, edited by Dr P. A. Pilavachi, 624-638. Springer Netherlands, 1993. doi:10.1007/978-94-011-1454-7_56.
- 2
Kandlikar, Satish G. Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier, 2006.
- 3
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.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.
- Parameters
- Returns
- De
float
Dean number [-]
- De
Notes
Used in flow in curved geometry.
References
- 1
Catchpole, John P., and George. Fulford. “DIMENSIONLESS GROUPS.” Industrial & Engineering Chemistry 58, no. 3 (March 1, 1966): 46-60. doi:10.1021/ie50675a012.
Examples
>>> Dean(10000, 0.1, 0.4) 5000.0
- fluids.core.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.
- Parameters
- Returns
- Cd
float
Drag coefficient, [-]
- Cd
Notes
Used in flow around objects, or objects flowing within a fluid.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Drag(1000, 0.0001, 5, 2000) 400.0
- fluids.core.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.
- Parameters
- Returns
- Ec
float
Eckert number []
- Ec
Notes
Used in certain heat transfer calculations. Fairly rare.
References
- 1
Goldstein, Richard J. ECKERT NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.e.eckert_number
Examples
>>> Eckert(10, 2000., 25.) 0.002
- fluids.core.Euler(dP, rho, V)[source]¶
Calculates Euler number or Eu for a fluid of velocity V and density rho experiencing a pressure drop dP.
- Parameters
- Returns
- Eu
float
Euler number []
- Eu
Notes
Used in pressure drop calculations. Rarely, this number is divided by two. Named after Leonhard Euler applied calculus to fluid dynamics.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Euler(1E5, 1000., 4) 6.25
- fluids.core.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.
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
- Returns
- Fo
float
Fourier number (heat) []
- Fo
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Fourier_heat(t=1.5, L=2, rho=1000., Cp=4000., k=0.6) 5.625e-08 >>> Fourier_heat(1.5, 2, alpha=1E-7) 3.75e-08
- fluids.core.Fourier_mass(t, L, D)[source]¶
Calculates mass transfer Fourier number or Fo for a specified time t, characteristic length L, and diffusion coefficient D.
- Parameters
- Returns
- Fo
float
Fourier number (mass) []
- Fo
Notes
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
Examples
>>> Fourier_mass(t=1.5, L=2, D=1E-9) 3.7500000000000005e-10
- fluids.core.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.
- Parameters
- Returns
- Fr
float
Froude number, [-]
- Fr
Notes
Many alternate definitions including density ratios have been used.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Froude(1.83, L=2., g=1.63) 1.0135432593877318 >>> Froude(1.83, L=2., squared=True) 0.17074638128208924
- fluids.core.Froude_densimetric(V, L, rho1, rho2, heavy=True, g=9.80665)[source]¶
Calculates the densimetric Froude number 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.
- 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]
- heavybool,
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]
- V
- Returns
- Fr_den
float
Densimetric Froude number, [-]
- Fr_den
Notes
Many alternate definitions including density ratios have been used.
Where the gravity force is reduced by the relative densities of one fluid in another.
Note that an Exception will be raised if rho1 > rho2, as the square root becomes negative.
References
- 1
Hall, A, G Stobie, and R Steven. “Further Evaluation of the Performance of Horizontally Installed Orifice Plate and Cone Differential Pressure Meters with Wet Gas Flows.” In International SouthEast Asia Hydrocarbon Flow Measurement Workshop, KualaLumpur, Malaysia, 2008.
Examples
>>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81) 0.4134543386272418 >>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81, heavy=False) 0.016013017679205096
- fluids.core.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.
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
- Returns
- Gz
float
Graetz number []
- Gz
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
Examples
>>> Graetz_heat(1.5, 0.25, 5, 800., 2200., 0.6) 55000.0 >>> Graetz_heat(1.5, 0.25, 5, alpha=1E-7) 187500.0
- fluids.core.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.
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]
- L
- Returns
- Gr
float
Grashof number []
- Gr
Notes
An error is raised if none of the required input sets are provided. Used in free convection problems only.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
Example 4 of [1], p. 1-21 (matches):
>>> Grashof(L=0.9144, beta=0.000933, T1=178.2, rho=1.1613, mu=1.9E-5) 4656936556.178915 >>> Grashof(L=0.9144, beta=0.000933, T1=378.2, T2=200, nu=1.636e-05) 4657491516.530312
- fluids.core.Hagen(Re, fd)[source]¶
Calculates Hagen number, Hg, for a fluid with the given Reynolds number and friction factor.
- Parameters
- Returns
- Hg
float
Hagen number, [-]
- Hg
Notes
Introduced in [1]; further use of it is mostly of the correlations introduced in [1].
Notable for use use in correlations, because it does not have any dependence on velocity.
This expression is useful when designing backwards with a pressure drop spec already known.
References
- 1(1,2)
Martin, Holger. “The Generalized Lévêque Equation and Its Practical Use for the Prediction of Heat and Mass Transfer Rates from Pressure Drop.” Chemical Engineering Science, Jean-Claude Charpentier Festschrift Issue, 57, no. 16 (August 1, 2002): 3217-23. https://doi.org/10.1016/S0009-2509(02)00194-X.
- 2
Shah, Ramesh K., and Dusan P. Sekulic. Fundamentals of Heat Exchanger Design. 1st edition. Hoboken, NJ: Wiley, 2002.
- 3
Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
Examples
Example from [3]:
>>> Hagen(Re=2610, fd=1.935235) 6591507.17175
- fluids.core.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.
- Parameters
- Returns
- Ja
float
Jakob number []
- Ja
Notes
Used in boiling heat transfer analysis. Fairly rare.
References
- 1
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Jakob(4000., 2E6, 10.) 0.02
- fluids.core.Knudsen(path, L)[source]¶
Calculates Knudsen number or Kn for a fluid with mean free path path and for a characteristic length L.
- Parameters
- Returns
- Kn
float
Knudsen number []
- Kn
Notes
Used in mass transfer calculations.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Knudsen(1e-10, .001) 1e-07
- fluids.core.Lewis(D=None, alpha=None, Cp=None, k=None, rho=None)[source]¶
Calculates Lewis number or Le for a fluid with the given parameters.
Inputs can be either of the following sets:
Diffusivity and Thermal diffusivity
Diffusivity, heat capacity, thermal conductivity, and density
- Parameters
- Returns
- Le
float
Lewis number []
- Le
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
- 3
Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
Examples
>>> Lewis(D=22.6E-6, alpha=19.1E-6) 0.8451327433628318 >>> Lewis(D=22.6E-6, rho=800., k=.2, Cp=2200) 0.00502815768302494
- fluids.core.Mach(V, c)[source]¶
Calculates Mach number or Ma for a fluid of velocity V with speed of sound c.
- Parameters
- Returns
- Ma
float
Mach number []
- Ma
Notes
Used in compressible flow calculations.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Mach(33., 330) 0.1
- fluids.core.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.
- Parameters
- Returns
- Mo
float
Morton number, [-]
- Mo
Notes
Used in modeling bubbles in liquid.
References
- 1
Kunes, Josef. Dimensionless Physical Quantities in Science and Engineering. Elsevier, 2012.
- 2
Yan, Xiaokang, Kaixin Zheng, Yan Jia, Zhenyong Miao, Lijun Wang, Yijun Cao, and Jiongtian Liu. “Drag Coefficient Prediction of a Single Bubble Rising in Liquids.” Industrial & Engineering Chemistry Research, April 2, 2018. https://doi.org/10.1021/acs.iecr.7b04743.
Examples
>>> Morton(1077.0, 76.5, 4.27E-3, 0.023) 2.311183104430743e-07
- fluids.core.Nusselt(h, L, k)[source]¶
Calculates Nusselt number Nu for a heat transfer coefficient h, characteristic length L, and thermal conductivity k.
- Parameters
- Returns
- Nu
float
Nusselt number, [-]
- Nu
Notes
Do not confuse k, the thermal conductivity of the fluid, with that of within a solid object associated with!
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
Examples
>>> Nusselt(1000., 1.2, 300.) 4.0 >>> Nusselt(10000., .01, 4000.) 0.025
- fluids.core.Ohnesorge(L, rho, mu, sigma)[source]¶
Calculates Ohnesorge number, Oh, for a fluid with the given characteristic length, density, viscosity, and surface tension.
- Parameters
- Returns
- Oh
float
Ohnesorge number []
- Oh
Notes
Often used in spray calculations. Sometimes given the symbol Z.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
Examples
>>> Ohnesorge(1E-4, 1000., 1E-3, 1E-1) 0.01
- fluids.core.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.
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
- Returns
- Pe
float
Peclet number (heat) []
- Pe
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Peclet_heat(1.5, 2, 1000., 4000., 0.6) 20000000.0 >>> Peclet_heat(1.5, 2, alpha=1E-7) 30000000.0
- fluids.core.Peclet_mass(V, L, D)[source]¶
Calculates mass transfer Peclet number or Pe for a specified velocity V, characteristic length L, and diffusion coefficient D.
- Parameters
- Returns
- Pe
float
Peclet number (mass) []
- Pe
Notes
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
Examples
>>> Peclet_mass(1.5, 2, 1E-9) 3000000000.0
- fluids.core.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.
- Parameters
- Returns
- Po
float
Power number []
- Po
Notes
Used in mixing calculations.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Power_number(P=180, L=0.01, N=2.5, rho=800.) 144000000.0
- fluids.core.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.
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
- Returns
- Pr
float
Prandtl number []
- Pr
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
- 3
Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
Examples
>>> Prandtl(Cp=1637., k=0.010, mu=4.61E-6) 0.754657 >>> Prandtl(Cp=1637., k=0.010, nu=6.4E-7, rho=7.1) 0.7438528 >>> Prandtl(nu=6.3E-7, alpha=9E-7) 0.7000000000000001
- fluids.core.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.
Notes
Used in free convection problems only.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Rayleigh(1.2, 4.6E9) 5520000000.0
- fluids.core.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.
- Parameters
- Returns
- eD
float
Relative Roughness, [-]
- eD
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> relative_roughness(0.5, 1E-4) 0.0002
- fluids.core.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.
Inputs either of any of the following sets:
V, D, density rho and dynamic viscosity mu
V, D, and kinematic viscosity nu
- Parameters
- Returns
- Re
float
Reynolds number []
- Re
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Reynolds(2.5, 0.25, 1.1613, 1.9E-5) 38200.65789473684 >>> Reynolds(2.5, 0.25, nu=1.636e-05) 38202.93398533008
- fluids.core.Schmidt(D, mu=None, nu=None, rho=None)[source]¶
Calculates Schmidt number or Sc for a fluid with the given parameters.
Inputs can be any of the following sets:
Diffusivity, dynamic viscosity, and density
Diffusivity and kinematic viscosity
- Parameters
- Returns
- Sc
float
Schmidt number []
- Sc
Notes
An error is raised if none of the required input sets are provided.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Schmidt(D=2E-6, mu=4.61E-6, rho=800) 0.00288125 >>> Schmidt(D=1E-9, nu=6E-7) 599.9999999999999
- fluids.core.Sherwood(K, L, D)[source]¶
Calculates Sherwood number Sh for a mass transfer coefficient K, characteristic length L, and diffusivity D.
- Parameters
- Returns
- Sh
float
Sherwood number, [-]
- Sh
Notes
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
Examples
>>> Sherwood(1000., 1.2, 300.) 4.0
- fluids.core.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 [1] [2].
- Parameters
- Returns
- St
float
Stanton number []
- St
Notes
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
Examples
>>> Stanton(5000, 5, 800, 2000.) 0.000625
- 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.
- Parameters
- Returns
- Stk
float
Stokes numer, [-]
- Stk
Notes
Used in droplet impaction or collection studies.
References
- 1
Rhodes, Martin J. Introduction to Particle Technology. Wiley, 2013.
- 2
Al-Dughaither, Abdullah S., Ahmed A. Ibrahim, and Waheed A. Al-Masry. “Investigating Droplet Separation Efficiency in Wire-Mesh Mist Eliminators in Bubble Column.” Journal of Saudi Chemical Society 14, no. 4 (October 1, 2010): 331-39. https://doi.org/10.1016/j.jscs.2010.04.001.
Examples
>>> Stokes_number(V=0.9, Dp=1E-5, D=1E-3, rhop=1000, mu=1E-5) 0.5
- fluids.core.Strouhal(f, L, V)[source]¶
Calculates Strouhal number St for a characteristic frequency f, characteristic length L, and velocity V.
- Parameters
- Returns
- St
float
Strouhal number, [-]
- St
Notes
Sometimes abbreviated to S or Sr.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> Strouhal(8, 2., 4.) 4.0
- fluids.core.Suratman(L, rho, mu, sigma)[source]¶
Calculates Suratman number, Su, for a fluid with the given characteristic length, density, viscosity, and surface tension.
- Parameters
- Returns
- Su
float
Suratman number []
- Su
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.
The oldest reference to this group found by the author is in 1963, from [2].
References
- 1
Sen, Nilava. “Suratman Number in Bubble-to-Slug Flow Pattern Transition under Microgravity.” Acta Astronautica 65, no. 3-4 (August 2009): 423-28. doi:10.1016/j.actaastro.2009.02.013.
- 2
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.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).
- Parameters
- Returns
- We
float
Weber number []
- We
Notes
Used in bubble calculations.
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
- 3
Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
Examples
>>> Weber(V=0.18, L=0.001, rho=900., sigma=0.01) 2.916
Loss Coefficient Converters¶
- fluids.core.K_from_f(fd, L, D)[source]¶
Calculates loss coefficient, K, for a given section of pipe at a specified friction factor.
- Parameters
- Returns
- K
float
Loss coefficient, []
- K
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).
- Parameters
- Returns
- K
float
Loss coefficient, []
- K
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.
- Parameters
- Returns
- L_D
float
Length over diameter, [-]
- L_D
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.
- Parameters
- Returns
- L
float
Length of pipe, [m]
- L
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.
- Parameters
- Returns
- dP
float
Pressure drop, [Pa]
- dP
Notes
Loss coefficient K is usually the sum of several factors, including the friction factor.
Examples
>>> dP_from_K(K=10, rho=1000, V=3) 45000.0
- fluids.core.head_from_K(K, V, g=9.80665)[source]¶
Calculates head loss, for a given loss coefficient, at a specified velocity.
- Parameters
- Returns
- head
float
Head loss, [m]
- head
Notes
Loss coefficient K is usually the sum of several factors, including the friction factor.
Examples
>>> head_from_K(K=10, V=1.5) 1.1471807396001694
- fluids.core.head_from_P(P, rho, g=9.80665)[source]¶
Calculates head for a fluid of specified density at specified pressure.
- Parameters
- Returns
- head
float
Head, [m]
- head
Notes
By definition. Head varies with location, inversely proportional to the increase in gravitational constant.
Examples
>>> head_from_P(P=98066.5, rho=1000) 10.000000000000002
- fluids.core.f_from_K(K, L, D)[source]¶
Calculates friction factor, fd, from a loss coefficient, K, for a given section of pipe.
- Parameters
- Returns
- fd
float
Darcy friction factor of pipe, [-]
- fd
Notes
This can be useful to blend fittings at specific locations in a pipe into a pressure drop which is evenly distributed along a pipe.
Examples
>>> f_from_K(K=0.6, L=100., D=.3) 0.0018
Temperature Conversions¶
These functions used to be part of SciPy, but were removed in favor of a slower function convert_temperature which removes code duplication but doesn’t have the same convenience or easy to remember signature.
- fluids.core.C2K(C)[source]¶
Convert Celsius to Kelvin.
- Parameters
- C
float
Celsius temperature to be converted, [degC]
- C
- Returns
- K
float
Equivalent Kelvin temperature, [K]
- K
Notes
Computes
K = C + zero_Celsius
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> C2K(-40) 233.14999999999998
- fluids.core.K2C(K)[source]¶
Convert Kelvin to Celsius.
Notes
Computes
C = K - zero_Celsius
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> K2C(233.15) -39.99999999999997
- fluids.core.F2C(F)[source]¶
Convert Fahrenheit to Celsius.
- Parameters
- F
float
Fahrenheit temperature to be converted.
- F
- Returns
- C
float
Equivalent Celsius temperature.
- C
Notes
Computes
C = (F - 32) / 1.8
.Examples
>>> F2C(-40.0) -40.0
- fluids.core.C2F(C)[source]¶
Convert Celsius to Fahrenheit.
- Parameters
- C
float
Celsius temperature to be converted.
- C
- Returns
- F
float
Equivalent Fahrenheit temperature.
- F
Notes
Computes
F = 1.8 * C + 32
.Examples
>>> C2F(-40.0) -40.0
- fluids.core.F2K(F)[source]¶
Convert Fahrenheit to Kelvin.
- Parameters
- F
float
Fahrenheit temperature to be converted.
- F
- Returns
- K
float
Equivalent Kelvin temperature.
- K
Notes
Computes
K = (F - 32)/1.8 + zero_Celsius
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> F2K(-40) 233.14999999999998
- fluids.core.K2F(K)[source]¶
Convert Kelvin to Fahrenheit.
- Parameters
- K
float
Kelvin temperature to be converted.
- K
- Returns
- F
float
Equivalent Fahrenheit temperature.
- F
Notes
Computes
F = 1.8 * (K - zero_Celsius) + 32
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> K2F(233.15) -39.99999999999996
- fluids.core.C2R(C)[source]¶
Convert Celsius to Rankine.
- Parameters
- C
float
Celsius temperature to be converted.
- C
- Returns
- Ra
float
Equivalent Rankine temperature.
- Ra
Notes
Computes
Ra = 1.8 * (C + zero_Celsius)
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> C2R(-40) 419.66999999999996
- fluids.core.K2R(K)[source]¶
Convert Kelvin to Rankine.
Notes
Computes
Ra = 1.8 * K
.Examples
>>> K2R(273.15) 491.66999999999996
- fluids.core.F2R(F)[source]¶
Convert Fahrenheit to Rankine.
- Parameters
- F
float
Fahrenheit temperature to be converted.
- F
- Returns
- Ra
float
Equivalent Rankine temperature.
- Ra
Notes
Computes
Ra = F - 32 + 1.8 * zero_Celsius
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> F2R(100) 559.67
- fluids.core.R2C(Ra)[source]¶
Convert Rankine to Celsius.
- Parameters
- Ra
float
Rankine temperature to be converted.
- Ra
- Returns
- C
float
Equivalent Celsius temperature.
- C
Notes
Computes
C = Ra / 1.8 - zero_Celsius
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> R2C(459.67) -17.777777777777743
- fluids.core.R2K(Ra)[source]¶
Convert Rankine to Kelvin.
Notes
Computes
K = Ra / 1.8
.Examples
>>> R2K(491.67) 273.15
- fluids.core.R2F(Ra)[source]¶
Convert Rankine to Fahrenheit.
- Parameters
- Ra
float
Rankine temperature to be converted.
- Ra
- Returns
- F
float
Equivalent Fahrenheit temperature.
- F
Notes
Computes
F = Ra + 32 - 1.8 * zero_Celsius
where zero_Celsius = 273.15, i.e., (the absolute value of) temperature “absolute zero” as measured in Celsius.Examples
>>> R2F(491.67) 32.00000000000006
Miscellaneous Functions¶
- fluids.core.thermal_diffusivity(k, rho, Cp)[source]¶
Calculates thermal diffusivity or alpha for a fluid with the given parameters.
- Parameters
- Returns
- alpha
float
Thermal diffusivity, [m^2/s]
- alpha
References
- 1
Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984.
Examples
>>> thermal_diffusivity(k=0.02, rho=1., Cp=1000.) 2e-05
- fluids.core.c_ideal_gas(T, k, MW)[source]¶
Calculates speed of sound c in an ideal gas at temperature T.
- Parameters
- Returns
- c
float
Speed of sound in fluid, [m/s]
- c
Notes
Used in compressible flow calculations. Note that the gas constant used is the specific gas constant:
References
- 1
Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.
- 2
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> c_ideal_gas(T=303, k=1.4, MW=28.96) 348.9820953185441
- 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.
- Parameters
- Returns
- mu or nu
float
Dynamic viscosity, Pa*s or Kinematic viscosity, m^2/s
- mu or nu
References
- 1
Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006.
Examples
>>> nu_mu_converter(998., nu=1.0E-6) 0.000998
- fluids.core.gravity(latitude, H)[source]¶
Calculates local acceleration due to gravity g according to [1]. Uses latitude and height to calculate g.
- Parameters
- Returns
- g
float
Acceleration due to gravity, [m/s^2]
- g
Notes
Better models, such as EGM2008 exist.
References
- 1
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