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# -*- coding: utf-8 -*- Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.'''
'Schmidt', 'Peclet_heat', 'Peclet_mass', 'Fourier_heat', 'Fourier_mass', 'Graetz_heat', 'Lewis', 'Weber', 'Mach', 'Knudsen', 'Bond', 'Dean', 'Froude', 'Strouhal', 'Biot', 'Stanton', 'Euler', 'Cavitation', 'Eckert', 'Jakob', 'Power_number', 'Drag', 'Capillary', 'Bejan_L', 'Bejan_p', 'Boiling', 'Confinement', 'Archimedes', 'Ohnesorge', 'Suratman', 'thermal_diffusivity', 'c_ideal_gas', 'relative_roughness', 'nu_mu_converter', 'gravity', 'K_from_f', 'K_from_L_equiv', 'L_equiv_from_K', 'dP_from_K', 'head_from_K', 'head_from_P', 'P_from_head', 'Eotvos']
### Not quite dimensionless groups r'''Calculates thermal diffusivity or `alpha` for a fluid with the given parameters.
.. math:: \alpha = \frac{k}{\rho Cp}
Parameters ---------- k : float Thermal conductivity, [W/m/K] Cp : float Heat capacity, [J/kg/K] rho : float Density, [kg/m^3]
Returns ------- alpha : float Thermal diffusivity, [m^2/s]
Notes -----
Examples -------- >>> thermal_diffusivity(0.02, 1., 1000.) 2e-05
References ---------- .. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.: Van Nostrand Reinhold Co., 1984. '''
### Ideal gas fluid properties
r'''Calculates speed of sound `c` in an ideal gas at temperature T.
.. math:: 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:
.. math:: R_{specific} = R\frac{1000}{MW}
Examples -------- >>> c_ideal_gas(1.4, 303., 28.96) 348.9820361755092
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. '''
### Dimensionless groups with documentation
r'''Calculates Reynolds number or `Re` for a fluid with the given properties for the specified velocity and diameter.
.. math:: 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 ---------- D : float Diameter [m] V : float Velocity [m/s] 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 ----- .. math:: Re = \frac{\text{Momentum}}{\text{Viscosity}}
An error is raised if none of the required input sets are provided.
Examples -------- >>> Reynolds(2.5, 0.25, 1.1613, 1.9E-5) 38200.65789473684 >>> Reynolds(2.5, 0.25, nu=1.636e-05) 38202.93398533008
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. ''' is needed')
r'''Calculates heat transfer Peclet number or `Pe` for a specified velocity `V`, characteristic length `L`, and specified properties for the given fluid.
.. math:: Pe = \frac{VL\rho C_p}{k} = \frac{LV}{\alpha}
Inputs either of any of the following sets:
* V, L, density `rho`, heat capcity `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 ----- .. math:: Pe = \frac{\text{Bulk heat transfer}}{\text{Conduction heat transfer}}
An error is raised if none of the required input sets are provided.
Examples -------- >>> Peclet_heat(1.5, 2, 1000., 4000., 0.6) 20000000.0 >>> Peclet_heat(1.5, 2, alpha=1E-7) 30000000.0
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. ''' density, or thermal diffusivity is needed')
r'''Calculates mass transfer Peclet number or `Pe` for a specified velocity `V`, characteristic length `L`, and diffusion coefficient `D`.
.. math:: 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 ----- .. math:: Pe = \frac{\text{Advective transport rate}}{\text{Diffusive transport rate}}
Examples -------- >>> Peclet_mass(1.5, 2, 1E-9) 3000000000.0
References ---------- .. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill Professional, 2007. '''
r'''Calculates heat transfer Fourier number or `Fo` for a specified time `t`, characteristic length `L`, and specified properties for the given fluid.
.. math:: 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 capcity `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 ----- .. math:: 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.
Examples -------- >>> Fourier_heat(1.5, 2, 1000., 4000., 0.6) 5.625e-08 >>> Fourier_heat(1.5, 2, alpha=1E-7) 3.75e-08
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. ''' density, or thermal diffusivity is needed')
r'''Calculates mass transfer Fourier number or `Fo` for a specified time `t`, characteristic length `L`, and diffusion coefficient `D`.
.. math:: 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 ----- .. math:: Fo = \frac{\text{Diffusive transport rate}}{\text{Storage rate}}
Examples -------- >>> Fourier_mass(1.5, 2, 1E-9) 3.7500000000000005e-10
References ---------- .. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill Professional, 2007. '''
r'''Calculates Graetz number or `Gz` for a specified velocity `V`, diameter `D`, axial diatance `x`, and specified properties for the given fluid.
.. math:: 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 capcity `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 ----- .. math:: 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.
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
References ---------- .. [1] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011. ''' density, or thermal diffusivity is needed')
r'''Calculates Schmidt number or `Sc` for a fluid with the given parameters.
.. math:: 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 ----- .. math:: 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.
Examples -------- >>> Schmidt(D=2E-6, mu=4.61E-6, rho=800) 0.00288125 >>> Schmidt(D=1E-9, nu=6E-7) 599.9999999999999
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. ''' else:
r'''Calculates Lewis number or `Le` for a fluid with the given parameters.
.. math:: 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 ----- .. math:: Le=\frac{\text{Thermal diffusivity}}{\text{Mass diffusivity}} = \frac{Sc}{Pr}
An error is raised if none of the required input sets are provided.
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
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. ''' else:
r'''Calculates Weber number, `We`, for a fluid with the given density, surface tension, velocity, and geometric parameter (usually diameter of bubble).
.. math:: 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.
.. math:: We = \frac{\text{inertial force}}{\text{surface tension force}}
Examples -------- >>> Weber(V=0.18, L=0.001, rho=900., sigma=0.01) 2.916
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. '''
r'''Calculates Mach number or `Ma` for a fluid of velocity `V` with speed of sound `c`.
.. math:: 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.
.. math:: Ma = \frac{\text{fluid velocity}}{\text{sonic velocity}}
Examples -------- >>> Mach(33., 330) 0.1
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. '''
r'''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`.
.. math:: \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 [1]_ according to [3]_.
.. math:: \text{Co} = \frac{\frac{\text{surface tension force}} {\text{buoyancy force}}}{\text{Channel area}}
Examples -------- >>> Confinement(0.001, 1077, 76.5, 4.27E-3) 0.6596978265315191
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. '''
r'''Calculates Knudsen number or `Kn` for a fluid with mean free path `path` and for a characteristic length `L`.
.. math:: 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.
.. math:: Kn = \frac{\text{Mean free path length}}{\text{Characteristic length}}
Examples -------- >>> Knudsen(1e-10, .001) 1e-07
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. '''
r'''Calculates Prandtl number or `Pr` for a fluid with the given parameters.
.. math:: 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 ----- .. math:: 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.
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
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. ''' else:
r'''Calculates Grashof number or `Gr` for a fluid with the given properties, temperature difference, and characteristic length.
.. math:: 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 ----- .. math:: 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.
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
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. ''' is needed')
r'''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).
.. math:: 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 []
Examples -------- >>> Bond(1000., 1.2, .0589, 2) 665187.2339558573
References ---------- .. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill Professional, 2007. '''
r'''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`.
.. math:: Ra = PrGr
Parameters ---------- Pr : float Prandtl number [] Gr : float Grashof number []
Returns ------- Ra : float Rayleigh number []
Notes ----- Used in free convection problems only.
Examples -------- >>> Rayleigh(1.2, 4.6E9) 5520000000.0
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. '''
r'''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.
.. math:: 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 Frounde number
Returns ------- Fr : float Froude number, [-]
Notes ----- Many alternate definitions including density ratios have been used.
.. math:: Fr = \frac{\text{Inertial Force}}{\text{Gravity Force}}
Examples -------- >>> Froude(1.83, L=2., g=1.63) 1.0135432593877318 >>> Froude(1.83, L=2., squared=True) 0.17074638128208924
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. '''
r'''Calculates Strouhal number `St` for a characteristic frequency `f`, characteristic length `L`, and velocity `V`.
.. math:: 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.
.. math:: St = \frac{\text{Characteristif flow time}} {\text{Period of oscillation}}
Examples -------- >>> Strouhal(8, 2., 4.) 4.0
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. '''
r'''Calculates Nusselt number `Nu` for a heat transfer coefficient `h`, characteristic length `L`, and thermal conductivity `k`.
.. math:: 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!
.. math:: Nu = \frac{\text{Convective heat transfer}} {\text{Conductive heat transfer}}
Examples -------- >>> Nusselt(1000., 1.2, 300.) 4.0 >>> Nusselt(10000., .01, 4000.) 0.025
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. '''
r'''Calculates Sherwood number `Sh` for a mass transfer coefficient `K`, characteristic length `L`, and diffusivity `D`.
.. math:: 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 -----
.. math:: Sh = \frac{\text{Mass transfer by convection}} {\text{Mass transfer by diffusion}} = \frac{K}{D/L}
Examples -------- >>> Sherwood(1000., 1.2, 300.) 4.0
References ---------- .. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill Professional, 2007. '''
r'''Calculates Biot number `Br` for heat transfer coefficient `h`, geometric length `L`, and thermal conductivity `k`.
.. math:: 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!
.. math:: Bi = \frac{\text{Surface thermal resistance}} {\text{Internal thermal resistance}}
Examples -------- >>> Biot(1000., 1.2, 300.) 4.0 >>> Biot(10000., .01, 4000.) 0.025
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. '''
r'''Calculates Stanton number or `St` for a specified heat transfer coefficient `h`, velocity `V`, density `rho`, and heat capacity `Cp`.
.. math:: 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 ----- .. math:: St = \frac{\text{Heat transfer coefficient}}{\text{Thermal capacity}}
Examples -------- >>> Stanton(5000, 5, 800, 2000.) 0.000625
References ---------- .. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill Professional, 2007. .. [1] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011. '''
r'''Calculates Euler number or `Eu` for a fluid of velocity `V` and density `rho` experiencing a pressure drop `dP`.
.. math:: 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.
.. math:: Eu = \frac{\text{Pressure drop}}{2\cdot \text{velocity head}}
Examples -------- >>> Euler(1E5, 1000., 4) 6.25
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. '''
r'''Calculates Cavitation number or `Ca` for a fluid of velocity `V` with a pressure `P`, vapor pressure `Psat`, and density `rho`.
.. math:: 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;
.. math:: Ca = \frac{\text{Pressure - Vapor pressure}} {\text{Inertial pressure}}
Examples -------- >>> Cavitation(2E5, 1E4, 1000, 10) 3.8
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. '''
r'''Calculates Eckert number or `Ec` for a fluid of velocity `V` with a heat capacity `Cp`, between two temperature given as `dT`.
.. math:: 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.
.. math:: Ec = \frac{\text{Kinetic energy} }{ \text{Enthalpy difference}}
Examples -------- >>> Eckert(10, 2000., 25.) 0.002
References ---------- .. [1] Goldstein, Richard J. ECKERT NUMBER. Thermopedia. Hemisphere, 2011. 10.1615/AtoZ.e.eckert_number '''
r'''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.
.. math:: 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.
.. math:: Ja = \frac{\Delta \text{Sensible heat}}{\Delta \text{Latent heat}}
Examples -------- >>> Jakob(4000., 2E6, 10.) 0.02
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. '''
r'''Calculates power number, `Po`, for an agitator applying a specified power `P` with a characteristic length `L`, rotationa speed `N`, to a fluid with a specified density `rho`.
.. math:: 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.
.. math:: Po = \frac{\text{Power}}{\text{Rotational inertia}}
Examples -------- >>> Power_number(P=180, L=0.01, N=2.5, rho=800.) 144000000.0
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. '''
r'''Calculates drag coefficient `Cd` for a given drag force `F`, projected area `A`, characteristic velocity `V`, and density `rho`.
.. math:: 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.
.. math:: C_D = \frac{\text{Drag forces}}{\text{Projected area}\cdot \text{Velocity head}}
Examples -------- >>> Drag(1000, 0.0001, 5, 2000) 400.0
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. '''
r'''Calculates Capillary number `Ca` for a characteristic velocity `V`, viscosity `mu`, and surface tension `sigma`.
.. math:: 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.
.. math:: Ca = \frac{\text{Viscous forces}} {\text{Surface forces}}
Examples -------- >>> Capillary(1.2, 0.01, .1) 0.12
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. '''
r'''Calculates Archimedes number, `Ar`, for a fluid and particle with the given densities, characteristic length, viscosity, and gravity (usually diameter of particle).
.. math:: 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.
.. math:: Ar = \frac{\text{Gravitational force}}{\text{Viscous force}}
Examples -------- >>> Archimedes(0.002, 2., 3000, 1E-3) 470.4053872
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. '''
r'''Calculates Ohnesorge number, `Oh`, for a fluid with the given characteristic length, density, viscosity, and surface tension.
.. math:: \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.
.. math:: Oh = \frac{\sqrt{\text{We}}}{\text{Re}}= \frac{\text{viscous forces}} {\sqrt{\text{Inertia}\cdot\text{Surface tension}} }
Examples -------- >>> Ohnesorge(1E-4, 1000., 1E-3, 1E-1) 0.01
References ---------- .. [1] Green, Don, and Robert Perry. Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill Professional, 2007. '''
r'''Calculates Suratman number, `Su`, for a fluid with the given characteristic length, density, viscosity, and surface tension.
.. math:: \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.
.. math:: \text{Su} = \frac{\text{Re}^2}{\text{We}} =\frac{\text{Inertia}\cdot \text{Surface tension} }{\text{(viscous forces)}^2}
The oldest reference to this group found by the author is in 1963, from [2]_.
Examples -------- >>> Suratman(1E-4, 1000., 1E-3, 1E-1) 10000.0
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. '''
r'''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`.
.. math:: 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.
Examples -------- >>> Bejan_L(1E4, 1, 1E-3, 1E-6) 10000000000000.0
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. '''
r'''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`.
.. math:: 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.
Examples -------- >>> Bejan_p(1E4, 1, 1E-3, 1E-6) 10000000000000.0
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. '''
r'''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.
.. math:: \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.
.. math:: \text{Bg} = \frac{\text{mass liquid evaporated / area heat transfer surface}}{\text{mass flow rate fluid / flow cross sectional area}}
First defined in [4]_, though not named.
Examples -------- >>> Boiling(300, 3000, 800000) 1.25e-05
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. '''
r'''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.
.. math:: \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.
.. math:: \text{De} = \frac{\sqrt{\text{centripetal forces}\cdot \text{inertial forces}}}{\text{viscous forces}}
Examples -------- >>> Dean(10000, 0.1, 0.4) 5000.0
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. '''
r'''Calculates relative roughness `eD` using a diameter and the roughness of the material of the wall. Default roughness is that of steel.
.. math:: eD=\frac{\epsilon}{D}
Parameters ---------- D : float Diameter of pipe, [m] roughness : float, optional Roughness of pipe wall [m]
Returns ------- eD : float Relative Roughness, [-]
Examples -------- >>> relative_roughness(0.5, 1E-4) 0.0002
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. '''
### Misc utilities
r'''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.
.. math:: \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]
Examples -------- >>> nu_mu_converter(998., nu=1.0E-6) 0.000998
References ---------- .. [1] Cengel, Yunus, and John Cimbala. Fluid Mechanics: Fundamentals and Applications. Boston: McGraw Hill Higher Education, 2006. '''
r'''Calculates local acceleration due to gravity `g` according to [1]_. Uses latitude and height to calculate `g`.
.. math:: 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.
Examples -------- >>> gravity(55, 1E4) 9.784151976863571
References ---------- .. [1] Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics. [Boca Raton, FL]: CRC press, 2014. '''
### Friction loss conversion functions
r'''Calculates loss coefficient, K, for a given section of pipe at a specified friction factor.
.. math:: 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 '''
r'''Calculates loss coefficient, for a given equivalent length (L/D).
.. math:: 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 '''
r'''Calculates equivalent length of pipe (L/D), for a given loss coefficient.
.. math:: \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 '''
r'''Calculates pressure drop, for a given loss coefficient, at a specified density and velocity.
.. math:: 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 ciefficient `K` is usually the sum of several factors, including the friction factor.
Examples -------- >>> dP_from_K(K=10, rho=1000, V=3) 45000.0 '''
r'''Calculates head loss, for a given loss coefficient, at a specified velocity.
.. math:: \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 ciefficient `K` is usually the sum of several factors, including the friction factor.
Examples -------- >>> head_from_K(K=10, V=1.5) 1.1471807396001694 '''
r'''Calculates head for a fluid of specified density at specified pressure.
.. math:: \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 propertional to the increase in gravitational constant.
Examples -------- >>> head_from_P(P=98066.5, rho=1000) 10.000000000000002 '''
r'''Calculates head for a fluid of specified density at specified pressure.
.. math:: 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]
Notes -----
Examples -------- >>> P_from_head(head=5., rho=800.) 39226.6 '''
### Synonyms |