Fittings pressure drop (fluids.fittings)¶

fluids.fittings.
contraction_sharp
(Di1, Di2)[source]¶ Returns loss coefficient for any sharp edged pipe contraction as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696(1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622(10.215\beta^2  0.785\beta^5)\\\beta = d_2/d_1\end{aligned}\end{align} \]Parameters:  Di1 : float
Inside diameter of original pipe, [m]
 Di2 : float
Inside diameter of following pipe, [m]
Returns:  K : float
Loss coefficient in terms of the following pipe []
Notes
A value of 0.506 or simply 0.5 is often used.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> contraction_sharp(Di1=1, Di2=0.4) 0.5301269161591805

fluids.fittings.
contraction_round
(Di1, Di2, rc)[source]¶ Returns loss coefficient for any round edged pipe contraction as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  0.569\frac{r}{d_2}\right)\left(1\sqrt{\frac{r} {d_2}}\beta\right)(1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left(1  0.30\sqrt{\frac{r}{d_2}}  0.70\frac{r}{d_2}\right)^4 (10.215\beta^20.785\beta^5)\\\beta = d_2/d_1\end{aligned}\end{align} \]Parameters:  Di1 : float
Inside diameter of original pipe, [m]
 Di2 : float
Inside diameter of following pipe, [m]
 rc : float
Radius of curvature of the contraction, [m]
Returns:  K : float
Loss coefficient in terms of the following pipe []
Notes
Rounding radius larger than 0.14Di2 prevents flow separation from the wall. Further increase in rounding radius continues to reduce loss coefficient.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> contraction_round(Di1=1, Di2=0.4, rc=0.04) 0.1783332490866574

fluids.fittings.
contraction_conical
(Di1, Di2, fd, l=None, angle=None)[source]¶ Returns loss coefficient for any conical pipe contraction as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696[1+C_B(\sin(\alpha/2)1)](1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622(\alpha/180)^{0.8}(10.215\beta^20.785\beta^5)\\\beta = d_2/d_1\end{aligned}\end{align} \]Parameters:  Di1 : float
Inside diameter of original pipe, [m]
 Di2 : float
Inside diameter of following pipe, [m]
 fd : float
Darcy friction factor []
 l : float
Length of the contraction, optional [m]
 angle : float
Angle of contraction, optional [degrees]
Returns:  K : float
Loss coefficient in terms of the following pipe []
Notes
Cheap and has substantial impact on pressure drop.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> contraction_conical(Di1=0.1, Di2=0.04, l=0.04, fd=0.0185) 0.15779041548350314

fluids.fittings.
contraction_beveled
(Di1, Di2, l=None, angle=None)[source]¶ Returns loss coefficient for any sharp beveled pipe contraction as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696[1+C_B(\sin(\alpha/2)1)](1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left[1+C_B\left(\left(\frac{\alpha}{180} \right)^{0.8}1\right)\right](10.215\beta^20.785\beta^5)\\C_B = \frac{l}{d_2}\frac{2\beta\tan(\alpha/2)}{1\beta}\\\beta = d_2/d_1\end{aligned}\end{align} \]Parameters:  Di1 : float
Inside diameter of original pipe, [m]
 Di2 : float
Inside diameter of following pipe, [m]
 l : float
Length of the bevel along the pipe axis ,[m]
 angle : float
Angle of bevel, [degrees]
Returns:  K : float
Loss coefficient in terms of the following pipe []
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> contraction_beveled(Di1=0.5, Di2=0.1, l=.7*.1, angle=120) 0.40946469413070485

fluids.fittings.
diffuser_sharp
(Di1, Di2)[source]¶ Returns loss coefficient for any sudden pipe diameter expansion as shown in [1] and in other sources.
\[K_1 = (1\beta^2)^2\]Parameters:  Di1 : float
Inside diameter of original pipe (smaller), [m]
 Di2 : float
Inside diameter of following pipe (larger), [m]
Returns:  K : float
Loss coefficient []
Notes
Highly accurate.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> diffuser_sharp(Di1=.5, Di2=1) 0.5625

fluids.fittings.
diffuser_conical
(Di1, Di2, l=None, angle=None, fd=None)[source]¶ Returns loss coefficient for any conical pipe expansion as shown in [1]. Five different formulas are used, depending on the angle and the ratio of diameters.
For 0 to 20 degrees, all aspect ratios:
\[K_1 = 8.30[\tan(\alpha/2)]^{1.75}(1\beta^2)^2 + \frac{f(1\beta^4)}{8\sin(\alpha/2)}\]For 20 to 60 degrees, beta < 0.5:
\[K_1 = \left\{1.366\sin\left[\frac{2\pi(\alpha15^\circ)}{180}\right]^{0.5}  0.170  3.28(0.0625\beta^4)\sqrt{\frac{\alpha20^\circ}{40^\circ}}\right\} (1\beta^2)^2 + \frac{f(1\beta^4)}{8\sin(\alpha/2)}\]For 20 to 60 degrees, beta >= 0.5:
\[K_1 = \left\{1.366\sin\left[\frac{2\pi(\alpha15^\circ)}{180}\right]^{0.5}  0.170 \right\}(1\beta^2)^2 + \frac{f(1\beta^4)}{8\sin(\alpha/2)}\]For 60 to 180 degrees, beta < 0.5:
\[K_1 = \left[1.205  3.28(0.0625\beta^4)12.8\beta^6\sqrt{\frac {\alpha60^\circ}{120^\circ}}\right](1\beta^2)^2\]For 60 to 180 degrees, beta >= 0.5:
\[K_1 = \left[1.205  0.20\sqrt{\frac{\alpha60^\circ}{120^\circ}} \right](1\beta^2)^2\]Parameters:  Di1 : float
Inside diameter of original pipe (smaller), [m]
 Di2 : float
Inside diameter of following pipe (larger), [m]
 l : float
Length of the contraction along the pipe axis, optional[m]
 angle : float
Angle of contraction, [degrees]
 fd : float
Darcy friction factor []
Returns:  K : float
Loss coefficient []
Notes
For angles above 60 degrees, friction factor is not used.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> diffuser_conical(Di1=1/3., Di2=1, angle=50, fd=0.03) 0.8081340270019336

fluids.fittings.
diffuser_conical_staged
(Di1, Di2, DEs, ls, fd=None)[source]¶ Returns loss coefficient for any series of staged conical pipe expansions as shown in [1]. Five different formulas are used, depending on the angle and the ratio of diameters. This function calls diffuser_conical.
Parameters:  Di1 : float
Inside diameter of original pipe (smaller), [m]
 Di2 : float
Inside diameter of following pipe (larger), [m]
 DEs : array
Diameters of intermediate sections, [m]
 ls : array
Lengths of the various sections, [m]
 fd : float
Darcy friction factor []
Returns:  K : float
Loss coefficient []
Notes
Only lengths of sections currently allowed. This could be changed to understand angles also.
Formula doesn’t make much sense, as observed by the example comparing a series of conical sections. Use only for small numbers of segments of highly differing angles.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> diffuser_conical(Di1=1., Di2=10.,l=9, fd=0.01) 0.973137914861591

fluids.fittings.
diffuser_curved
(Di1, Di2, l)[source]¶ Returns loss coefficient for any curved wall pipe expansion as shown in [1].
\[ \begin{align}\begin{aligned}K_1 = \phi(1.431.3\beta^2)(1\beta^2)^2\\\phi = 1.01  0.624\frac{l}{d_1} + 0.30\left(\frac{l}{d_1}\right)^2  0.074\left(\frac{l}{d_1}\right)^3 + 0.0070\left(\frac{l}{d_1}\right)^4\end{aligned}\end{align} \]Parameters:  Di1 : float
Inside diameter of original pipe (smaller), [m]
 Di2 : float
Inside diameter of following pipe (larger), [m]
 l : float
Length of the curve along the pipe axis, [m]
Returns:  K : float
Loss coefficient []
Notes
Beta^2 should be between 0.1 and 0.9. A small mismatch between tabulated values of this function in table 11.3 is observed with the equation presented.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> diffuser_curved(Di1=.25**0.5, Di2=1., l=2.) 0.2299781250000002

fluids.fittings.
diffuser_pipe_reducer
(Di1, Di2, l, fd1, fd2=None)[source]¶ Returns loss coefficient for any pipe reducer pipe expansion as shown in [1]. This is an approximate formula.
\[ \begin{align}\begin{aligned}K_f = f_1\frac{0.20l}{d_1} + \frac{f_1(1\beta)}{8\sin(\alpha/2)} + f_2\frac{0.20l}{d_2}\beta^4\\\alpha = 2\tan^{1}\left(\frac{d_1d_2}{1.20l}\right)\end{aligned}\end{align} \]Parameters:  Di1 : float
Inside diameter of original pipe (smaller), [m]
 Di2 : float
Inside diameter of following pipe (larger), [m]
 l : float
Length of the pipe reducer along the pipe axis, [m]
 fd1 : float
Darcy friction factor at inlet diameter []
 fd2 : float
Darcy friction factor at outlet diameter, optional []
Returns:  K : float
Loss coefficient []
Notes
Industry lack of standardization prevents better formulas from being developed. Add 15% if the reducer is eccentric. Friction factor at outlet will be assumed the same as at inlet if not specified.
Doubt about the validity of this equation is raised.
References
[1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> diffuser_pipe_reducer(Di1=.5, Di2=.75, l=1.5, fd1=0.07) 0.06873244301714816

fluids.fittings.
entrance_sharp
()[source]¶ Returns loss coefficient for a sharp entrance to a pipe as shown in [1].
\[K = 0.57\]Returns:  K : float
Loss coefficient []
Notes
Other values used have been 0.5.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> entrance_sharp() 0.57

fluids.fittings.
entrance_distance
(Di, t)[source]¶ Returns loss coefficient for a sharp entrance to a pipe at a distance from the wall of a reservoir, as shown in [1].
\[K = 1.12  22\frac{t}{d} + 216\left(\frac{t}{d}\right)^2 + 80\left(\frac{t}{d}\right)^3\]Parameters:  Di : float
Inside diameter of pipe, [m]
 t : float
Thickness of pipe wall, [m]
Returns:  K : float
Loss coefficient []
Notes
Recommended for cases where the length of the inlet pipe extending into a tank divided by the inner diameter of the pipe is larger than 0.5. If the pipe is 10 cm in diameter, the pipe should extend into the tank at least 5 cm. This type of inlet is also known as a Borda’s mouthpiece. It is not of practical interest according to [1].
If the pipe wall thickness to diameter ratio t/Di is larger than 0.05, it is rounded to 0.05; the effect levels off at that ratio and K=0.57.
References
[1] (1, 2, 3) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> entrance_distance(Di=0.1, t=0.0005) 1.0154100000000001

fluids.fittings.
entrance_angled
(angle)[source]¶ Returns loss coefficient for a sharp, angled entrance to a pipe flush with the wall of a reservoir, as shown in [1].
\[K = 0.57 + 0.30\cos(\theta) + 0.20\cos(\theta)^2\]Parameters:  angle : float
Angle of inclination (90=straight, 0=parallel to pipe wall) [degrees]
Returns:  K : float
Loss coefficient []
Notes
Not reliable for angles under 20 degrees. Loss coefficient is the same for an upward or downward angled inlet.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> entrance_angled(30) 0.9798076211353316

fluids.fittings.
entrance_rounded
(Di, rc)[source]¶ Returns loss coefficient for a rounded entrance to a pipe flush with the wall of a reservoir, as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  0.569\frac{r}{d}\right)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left(1  0.30\sqrt{\frac{r}{d}}  0.70\frac{r}{d}\right)^4\end{aligned}\end{align} \]Parameters:  Di : float
Inside diameter of pipe, [m]
 rc : float
Radius of curvature of the entrance, [m]
Returns:  K : float
Loss coefficient []
Notes
For generously rounded entrance (rc/Di >= 1), the loss coefficient converges to 0.03.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> entrance_rounded(Di=0.1, rc=0.0235) 0.09839534618360923

fluids.fittings.
entrance_beveled
(Di, l, angle)[source]¶ Returns loss coefficient for a beveled or chamfered entrance to a pipe flush with the wall of a reservoir, as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  C_b\frac{l}{d}\right)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left[11.5C_b\left(\frac{l}{d} \right)^{\frac{1(l/d)^{1/4}}{2}}\right]\\C_b = \left(1  \frac{\theta}{90}\right)\left(\frac{\theta}{90} \right)^{\frac{1}{1+l/d}}\end{aligned}\end{align} \]Parameters:  Di : float
Inside diameter of pipe, [m]
 l : float
Length of bevel measured parallel to the pipe length, [m]
 angle : float
Angle of bevel with respect to the pipe length, [degrees]
Returns:  K : float
Loss coefficient []
Notes
A cheap way of getting a lower pressure drop. Little credible data is available.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> entrance_beveled(Di=0.1, l=0.003, angle=45) 0.45086864221916984

fluids.fittings.
entrance_beveled_orifice
(Di, do, l, angle)[source]¶ Returns loss coefficient for a beveled or chamfered orifice entrance to a pipe flush with the wall of a reservoir, as shown in [1].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  C_b\frac{l}{d_o}\right)\lambda^2 + \left(\lambda \left(\frac{d_o}{D_i}\right)^2\right)^2\\\lambda = 1 + 0.622\left[1C_b\left(\frac{l}{d_o}\right)^{\frac{1 (l/d_o)^{0.25}}{2}}\right]\\C_b = \left(1  \frac{\Psi}{90}\right)\left(\frac{\Psi}{90} \right)^{\frac{1}{1+l/d_o}}\end{aligned}\end{align} \]Parameters:  Di : float
Inside diameter of pipe, [m]
 do : float
Inside diameter of orifice, [m]
 l : float
Length of bevel measured parallel to the pipe length, [m]
 angle : float
Angle of bevel with respect to the pipe length, [degrees]
Returns:  K : float
Loss coefficient []
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> entrance_beveled_orifice(Di=0.1, do=.07, l=0.003, angle=45) 1.2987552913818574

fluids.fittings.
exit_normal
()[source]¶ Returns loss coefficient for any exit to a pipe as shown in [1] and in other sources.
\[K = 1\]Returns:  K : float
Loss coefficient []
Notes
It has been found on occasion that K = 2.0 for laminar flow, and ranges from about 1.04 to 1.10 for turbulent flow.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> exit_normal() 1.0

fluids.fittings.
bend_rounded
(Di, angle, fd, rc=None, bend_diameters=5)[source]¶ Returns loss coefficient for any rounded bend in a pipe as shown in [1].
\[K = f\alpha\frac{r}{d} + (0.10 + 2.4f)\sin(\alpha/2) + \frac{6.6f(\sqrt{\sin(\alpha/2)}+\sin(\alpha/2))} {(r/d)^{\frac{4\alpha}{\pi}}}\]Parameters:  Di : float
Inside diameter of pipe, [m]
 angle : float
Angle of bend, [degrees]
 fd : float
Darcy friction factor []
 rc : float, optional
Radius of curvature of the entrance, optional [m]
 bend_diameters : float, optional (used if rc not provided)
Number of diameters of pipe making up the bend radius []
Returns:  K : float
Loss coefficient []
Notes
When inputting bend diameters, note that manufacturers often specify this as a multiplier of nominal diameter, which is different than actual diameter. Those require that rc be specified.
First term represents surface friction loss; the second, secondary flows; and the third, flow separation. Encompasses the entire range of elbow and pipe bend configurations.
This was developed for bend angles between 0 and 180 degrees; and r/D ratios above 0.5.
Note the loss coefficient includes the surface friction of the pipe as if it was straight.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> bend_rounded(Di=4.020, rc=4.0*5, angle=30, fd=0.0163) 0.10680196344492195

fluids.fittings.
bend_miter
(angle)[source]¶ Returns loss coefficient for any singlejoint miter bend in a pipe as shown in [1].
\[K = 0.42\sin(\alpha/2) + 2.56\sin^3(\alpha/2)\]Parameters:  angle : float
Angle of bend, [degrees]
Returns:  K : float
Loss coefficient []
Notes
Applies for bends from 0 to 150 degrees. One joint only.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> bend_miter(150) 2.7128147734758103

fluids.fittings.
helix
(Di, rs, pitch, N, fd)[source]¶ Returns loss coefficient for any size constantpitch helix as shown in [1]. Has applications in immersed coils in tanks.
\[K = N \left[f\frac{\sqrt{(2\pi r)^2 + p^2}}{d} + 0.20 + 4.8 f\right]\]Parameters:  Di : float
Inside diameter of pipe, [m]
 rs : float
Radius of spiral, [m]
 pitch : float
Distance between two subsequent coil centers, [m]
 N : float
Number of coils in the helix []
 fd : float
Darcy friction factor []
Returns:  K : float
Loss coefficient []
Notes
Formulation based on peak secondary flow as in two 180 degree bends per coil. Flow separation ignored. No f, Re, geometry limitations. Source not compared against others.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> helix(Di=0.01, rs=0.1, pitch=.03, N=10, fd=.0185) 14.525134924495514

fluids.fittings.
spiral
(Di, rmax, rmin, pitch, fd)[source]¶ Returns loss coefficient for any size constantpitch spiral as shown in [1]. Has applications in immersed coils in tanks.
\[K = \frac{r_{max}  r_{min}}{p} \left[ f\pi\left(\frac{r_{max} +r_{min}}{d}\right) + 0.20 + 4.8f\right] + \frac{13.2f}{(r_{min}/d)^2}\]Parameters:  Di : float
Inside diameter of pipe, [m]
 rmax : float
Radius of spiral at extremity, [m]
 rmin : float
Radius of spiral at end near center, [m]
 pitch : float
Distance between two subsequent coil centers, [m]
 fd : float
Darcy friction factor []
Returns:  K : float
Loss coefficient []
Notes
Source not compared against others.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> spiral(Di=0.01, rmax=.1, rmin=.02, pitch=.01, fd=0.0185) 7.950918552775473

fluids.fittings.
Darby3K
(NPS=None, Re=None, name=None, K1=None, Ki=None, Kd=None)[source]¶ Returns loss coefficient for any various fittings, depending on the name input. Alternatively, the Darby constants K1, Ki and Kd may be provided and used instead. Source of data is [1]. Reviews of this model are favorable.
\[K_f = \frac{K_1}{Re} + K_i\left(1 + \frac{K_d}{D_{\text{NPS}}^{0.3}} \right)\]Note this model uses nominal pipe diameter in inches.
Parameters:  NPS : float
Nominal diameter of the pipe, [in]
 Re : float
Reynolds number, []
 name : str
String from Darby dict representing a fitting
 K1 : float
K1 parameter of Darby model, optional []
 Ki : float
Ki parameter of Darby model, optional []
 Kd : float
Kd parameter of Darby model, optional [in]
Returns:  K : float
Loss coefficient []
Notes
Also described in Albright’s Handbook and Ludwig’s Applied Process Design. Relatively uncommon to see it used.
The possibility of combining these methods with those above are attractive.
References
[1] (1, 2) Silverberg, Peter, and Ron Darby. “Correlate Pressure Drops through Fittings: Three Constants Accurately Calculate Flow through Elbows, Valves and Tees.” Chemical Engineering 106, no. 7 (July 1999): 101. [2] Silverberg, Peter. “Correlate Pressure Drops Through Fittings.” Chemical Engineering 108, no. 4 (April 2001): 127,129130. Examples
>>> Darby3K(NPS=2., Re=10000., name='Valve, Angle valve, 45°, full line size, β = 1') 1.1572523963562353 >>> Darby3K(NPS=12., Re=10000., K1=950, Ki=0.25, Kd=4) 0.819510280626355

fluids.fittings.
Hooper2K
(Di, Re, name=None, K1=None, Kinfty=None)[source]¶ Returns loss coefficient for any various fittings, depending on the name input. Alternatively, the Hooper constants K1, Kinfty may be provided and used instead. Source of data is [1]. Reviews of this model are favorable less favorable than the Darby method but superior to the constantK method.
\[K = \frac{K_1}{Re} + K_\infty\left(1 + \frac{1\text{ inch}}{D_{in}}\right)\]Note this model uses actual inside pipe diameter in inches.
Parameters:  Di : float
Actual inside diameter of the pipe, [in]
 Re : float
Reynolds number, []
 name : str, optional
String from Hooper dict representing a fitting
 K1 : float, optional
K1 parameter of Hooper model, optional []
 Kinfty : float, optional
Kinfty parameter of Hooper model, optional []
Returns:  K : float
Loss coefficient []
Notes
Also described in Ludwig’s Applied Process Design. Relatively uncommon to see it used. No actual example found.
References
[1] (1, 2) Hooper, W. B., “The 2K Method Predicts Head Losses in Pipe Fittings,” Chem. Eng., p. 97, Aug. 24 (1981). [2] Hooper, William B. “Calculate Head Loss Caused by Change in Pipe Size.” Chemical Engineering 95, no. 16 (November 7, 1988): 89. [3] Kayode Coker. Ludwig’s Applied Process Design for Chemical and Petrochemical Plants. 4E. Amsterdam ; Boston: Gulf Professional Publishing, 2007. Examples
>>> Hooper2K(Di=2., Re=10000., name='Valve, Globe, Standard') 6.15 >>> Hooper2K(Di=2., Re=10000., K1=900, Kinfty=4) 6.09

fluids.fittings.
Kv_to_Cv
(Kv)[source]¶ Convert valve flow coefficient from imperial to common metric units.
\[C_v = 1.156 K_v\]Parameters:  Kv : float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
Returns:  Cv : float
Imperial Cv valve flow coefficient (flow rate of water at a pressure drop of 1 psi) [gallons/minute]
Notes
Kv = 0.865 Cv is in the IEC standard 6053421. It has also been said that Cv = 1.17Kv; this is wrong by current standards.
The conversion factor does not depend on the density of the fluid or the diameter of the valve. It is calculated with the definition of a US gallon as 231 cubic inches, and a psi as a poundforce per square inch.
The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.
References
[1] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> Kv_to_Cv(2) 2.3121984567073133

fluids.fittings.
Cv_to_Kv
(Cv)[source]¶ Convert valve flow coefficient from imperial to common metric units.
\[K_v = C_v/1.156\]Parameters:  Cv : float
Imperial Cv valve flow coefficient (flow rate of water at a pressure drop of 1 psi) [gallons/minute]
Returns:  Kv : float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
Notes
Kv = 0.865 Cv is in the IEC standard 6053421. It has also been said that Cv = 1.17Kv; this is wrong by current standards.
The conversion factor does not depend on the density of the fluid or the diameter of the valve. It is calculated with the definition of a US gallon as 231 cubic inches, and a psi as a poundforce per square inch.
The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.
References
[1] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> Cv_to_Kv(2.312) 1.9998283393826013

fluids.fittings.
Kv_to_K
(Kv, D)[source]¶ Convert valve flow coefficient from common metric units to regular loss coefficients.
\[K = 1.6\times 10^9 \frac{D^4}{K_v^2}\]Parameters:  Kv : float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
 D : float
Inside diameter of the valve [m]
Returns:  K : float
Loss coefficient, []
Notes
Crane TP 410 M (2009) gives the coefficient of 0.04 (with diameter in mm).
It also suggests the density of water should be found between 540°C. Older versions specify the density should be found at 60 °F, which is used here, and the pessure for the appropriate density is back calculated.
\[ \begin{align}\begin{aligned}\Delta P = 1 \text{ bar} = \frac{1}{2}\rho V^2\cdot K\\V = \frac{\frac{K_v\cdot \text{ hour}}{3600 \text{ second}}}{\frac{\pi}{4}D^2}\\\rho = 999.29744568 \;\; kg/m^3 \text{ at } T=60° F, P = 703572 Pa\end{aligned}\end{align} \]The value of density is calculated with IAPWS95; it is chosen as it makes the coefficient a very convenient round number. Others constants that have been used are 1.604E9, and 1.60045E9.
References
[1] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> Kv_to_K(2.312, .015) 15.153374600399898

fluids.fittings.
K_to_Kv
(K, D)[source]¶ Convert regular loss coefficient to valve flow coefficient.
\[K_v = 4\times 10^4 \sqrt{ \frac{D^4}{K}}\]Parameters:  K : float
Loss coefficient, []
 D : float
Inside diameter of the valve [m]
Returns:  Kv : float
Metric Kv valve flow coefficient (flow rate of water at a pressure drop of 1 bar) [m^3/hr]
Notes
Crane TP 410 M (2009) gives the coefficient of 0.04 (with diameter in mm).
It also suggests the density of water should be found between 540°C. Older versions specify the density should be found at 60 °F, which is used here, and the pessure for the appropriate density is back calculated.
\[ \begin{align}\begin{aligned}\Delta P = 1 \text{ bar} = \frac{1}{2}\rho V^2\cdot K\\V = \frac{\frac{K_v\cdot \text{ hour}}{3600 \text{ second}}}{\frac{\pi}{4}D^2}\\\rho = 999.29744568 \;\; kg/m^3 \text{ at } T=60° F, P = 703572 Pa\end{aligned}\end{align} \]The value of density is calculated with IAPWS95; it is chosen as it makes the coefficient a very convenient round number. Others constants that have been used are 1.604E9, and 1.60045E9.
References
[1] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> K_to_Kv(15.15337460039990, .015) 2.312

fluids.fittings.
Cv_to_K
(Cv, D)[source]¶ Convert imperial valve flow coefficient from imperial units to regular loss coefficients.
\[K = 1.6\times 10^9 \frac{D^4}{\left(\frac{C_v}{1.56}\right)^2}\]Parameters:  Cv : float
Imperial Cv valve flow coefficient (flow rate of water at a pressure drop of 1 psi) [gallons/minute]
 D : float
Inside diameter of the valve [m]
Returns:  K : float
Loss coefficient, []
Notes
The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.
References
[1] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> Cv_to_K(2.712, .015) 14.719595348352552

fluids.fittings.
K_to_Cv
(K, D)[source]¶ Convert regular loss coefficient to imperial valve flow coefficient.
\[K_v = 1.156 \cdot 4\times 10^4 \sqrt{ \frac{D^4}{K}}\]Parameters:  K : float
Loss coefficient, []
 D : float
Inside diameter of the valve [m]
Returns:  Cv : float
Imperial Cv valve flow coefficient (flow rate of water at a pressure drop of 1 psi) [gallons/minute]
Notes
The conversion factor does not depend on the density of the fluid or the diameter of the valve. It is calculated with the definition of a US gallon as 231 cubic inches, and a psi as a poundforce per square inch.
The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.
References
[1] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> K_to_Cv(16, .015) 2.601223263795727

fluids.fittings.
change_K_basis
(K1, D1, D2)[source]¶ Converts a loss coefficient K1 from the basis of one diameter D1 to another diameter, D2. This is necessary when dealing with pipelines of changing diameter.
\[K_2 = K_1\frac{D_2^4}{D_1^4} = K_1 \frac{A_2^2}{A_1^2}\]Parameters:  K1 : float
Loss coefficient with respect to diameter D, []
 D1 : float
Diameter of pipe for which K1 has been calculated, [m]
 D2 : float
Diameter of pipe for which K2 will be calculated, [m]
Returns:  K2 : float
Loss coefficient with respect to the second diameter, []
Notes
This expression is shown in [1] and can easily be derived:
\[\frac{\rho V_{1}^{2}}{2} \cdot K_{1} = \frac{\rho V_{2}^{2} }{2} \cdot K_{2} \]Substitute velocities for flow rate divided by area:
\[\frac{8 K_{1} Q^{2} \rho}{\pi^{2} D_{1}^{4}} = \frac{8 K_{2} Q^{2} \rho}{\pi^{2} D_{2}^{4}}\]From here, simplification and rearrangement is all that is required.
References
[1] (1, 2) Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012. Examples
>>> change_K_basis(K1=32.68875692997804, D1=.01, D2=.02) 523.0201108796487

fluids.fittings.
K_gate_valve_Crane
(D1, D2, angle, fd)[source]¶ Returns loss coefficient for a gate valve of types wedge disc, double disc, or plug type, as shown in [1].
If β = 1 and θ = 0:
\[K = K_1 = K_2 = 8f_d\]If β < 1 and θ <= 45°:
\[K_2 = \frac{K + \sin \frac{\theta}{2} \left[0.8(1\beta^2) + 2.6(1\beta^2)^2\right]}{\beta^4}\]If β < 1 and θ > 45°:
\[K_2 = \frac{K + 0.5\sqrt{\sin\frac{\theta}{2}}(1\beta^2) + (1\beta^2)^2}{\beta^4}\]Parameters:  D1 : float
Diameter of the valve seat bore (must be smaller or equal to D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 angle : float
Angle formed by the reducer in the valve, [degrees]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions [2].
References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. [2] (1, 2) Harvey Wilson. “Pressure Drop in Pipe Fittings and Valves  Equivalent Length and Resistance Coefficient.” Katmar Software. Accessed July 28, 2017. http://www.katmarsoftware.com/articles/pipefittingpressuredrop.htm. Examples
Example 74 in [1]; a 150 by 100 mm glass 600 steel gate valve, conically tapered ports, length 550 mm, back of sear ring ~150 mm. The valve is connected to 146 mm schedule 80 pipe. The angle can be calculated to be 13 degrees. The valve is specified to be operating in turbulent conditions.
>>> K_gate_valve_Crane(D1=.1, D2=.146, angle=13.115, fd=0.015) 1.145830368873396
The calculated result is lower than their value of 1.22; the difference is due to intermediate rounding.

fluids.fittings.
K_angle_valve_Crane
(D1, D2, fd, style=0)[source]¶ Returns the loss coefficient for all types of angle valve, (reduced seat or throttled) as shown in [1].
If β = 1:
\[K = K_1 = K_2 = N\cdot f_d\]Otherwise:
\[K_2 = \frac{K + \left[0.5(1\beta^2) + (1\beta^2)^2\right]}{\beta^4}\]For style 0 and 2, N = 55; for style 1, N=150.
Parameters:  D1 : float
Diameter of the valve seat bore (must be smaller or equal to D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
One of 0, 1, or 2; refers to three different types of angle valves as shown in [1] []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_angle_valve_Crane(.01, .02, fd=.016) 19.58

fluids.fittings.
K_globe_valve_Crane
(D1, D2, fd)[source]¶ Returns the loss coefficient for all types of globe valve, (reduced seat or throttled) as shown in [1].
If β = 1:
\[K = K_1 = K_2 = 340 f_d\]Otherwise:
\[K_2 = \frac{K + \left[0.5(1\beta^2) + (1\beta^2)^2\right]}{\beta^4}\]Parameters:  D1 : float
Diameter of the valve seat bore (must be smaller or equal to D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_globe_valve_Crane(.01, .02, fd=.015) 87.1

fluids.fittings.
K_swing_check_valve_Crane
(fd, angled=True)[source]¶ Returns the loss coefficient for a swing check valve as shown in [1].
\[K_2 = N\cdot f_d\]For angled swing check valves N = 100; for straight valves, N = 50.
Parameters:  fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 angled : bool, optional
If True, returns a value 2x the unangled value; the style of the valve []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_swing_check_valve_Crane(fd=.016) 1.6

fluids.fittings.
K_lift_check_valve_Crane
(D1, D2, fd, angled=True)[source]¶ Returns the loss coefficient for a lift check valve as shown in [1].
If β = 1:
\[K = K_1 = K_2 = N\cdot f_d\]Otherwise:
\[K_2 = \frac{K + \left[0.5(1\beta^2) + (1\beta^2)^2\right]}{\beta^4}\]For angled lift check valves N = 55; for straight valves, N = 600.
Parameters:  D1 : float
Diameter of the valve seat bore (must be smaller or equal to D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 angled : bool, optional
If True, returns a value 2x the unangled value; the style of the valve []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_lift_check_valve_Crane(.01, .02, fd=.016) 21.58

fluids.fittings.
K_tilting_disk_check_valve_Crane
(D, angle, fd)[source]¶ Returns the loss coefficient for a tilting disk check valve as shown in [1]. Results are specified in [1] to be for the disk’s resting position to be at 5 or 25 degrees to the flow direction. The model is implemented here so as to switch to the higher loss 15 degree coefficients at 10 degrees, and use the lesser coefficients for any angle under 10 degrees.
\[K = N\cdot f_d\]N is obtained from the following table:
angle = 5 ° angle = 15° 28” 40 120 1014” 30 90 1648” 20 60 The actual change of coefficients happen at <= 9” and <= 15”.
Parameters:  D : float
Diameter of the pipe section the valve in mounted in; the same as the line size [m]
 angle : float
Angle of the tilting disk to the flow direction; nominally 5 or 15 degrees [degrees]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_tilting_disk_check_valve_Crane(.01, 5, fd=.016) 0.64

fluids.fittings.
K_globe_stop_check_valve_Crane
(D1, D2, fd, style=0)[source]¶ Returns the loss coefficient for a globe stop check valve as shown in [1].
If β = 1:
\[K = K_1 = K_2 = N\cdot f_d\]Otherwise:
\[K_2 = \frac{K + \left[0.5(1\beta^2) + (1\beta^2)^2\right]}{\beta^4}\]Style 0 is the standard form; style 1 is angled, with a restrition to force the flow up through the valve; style 2 is also angled but with a smaller restriction forcing the flow up. N is 400, 300, and 55 for those cases respectively.
Parameters:  D1 : float
Diameter of the valve seat bore (must be smaller or equal to D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
One of 0, 1, or 2; refers to three different types of angle valves as shown in [1] []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_globe_stop_check_valve_Crane(.1, .02, .0165, style=1) 4.51992

fluids.fittings.
K_angle_stop_check_valve_Crane
(D1, D2, fd, style=0)[source]¶ Returns the loss coefficient for a angle stop check valve as shown in [1].
If β = 1:
\[K = K_1 = K_2 = N\cdot f_d\]Otherwise:
\[K_2 = \frac{K + \left[0.5(1\beta^2) + (1\beta^2)^2\right]}{\beta^4}\]Style 0 is the standard form; style 1 has a restrition to force the flow up through the valve; style 2 is has the clearest flow area with no guides for the angle valve. N is 200, 350, and 55 for those cases respectively.
Parameters:  D1 : float
Diameter of the valve seat bore (must be smaller or equal to D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
One of 0, 1, or 2; refers to three different types of angle valves as shown in [1] []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_angle_stop_check_valve_Crane(.1, .02, .0165, style=1) 4.52124

fluids.fittings.
K_ball_valve_Crane
(D1, D2, angle, fd)[source]¶ Returns the loss coefficient for a ball valve as shown in [1].
If β = 1:
\[K = K_1 = K_2 = 3f_d\]If β < 1 and θ <= 45°:
\[K_2 = \frac{K + \sin \frac{\theta}{2} \left[0.8(1\beta^2) + 2.6(1\beta^2)^2\right]} {\beta^4}\]If β < 1 and θ > 45°:
\[K_2 = \frac{K + 0.5\sqrt{\sin\frac{\theta}{2}}(1\beta^2) + (1\beta^2)^2}{\beta^4}\]Parameters:  D1 : float
Diameter of the valve seat bore (must be equal to or smaller than D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 angle : float
Angle formed by the reducer in the valve, [degrees]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_ball_valve_Crane(.01, .02, 50, .025) 14.100545785228675

fluids.fittings.
K_diaphragm_valve_Crane
(fd, style=0)[source]¶ Returns the loss coefficient for a diaphragm valve of either weir (style = 0) or straightthrough (style = 1) as shown in [1].
\[K = K_1 = K_2 = N\cdot f_d\]For style 0 (weir), N = 149; for style 1 (straight through), N = 39.
Parameters:  fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
Either 0 (weir type valve) or 1 (straight through weir valve) []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_diaphragm_valve_Crane(0.015, style=0) 2.235

fluids.fittings.
K_foot_valve_Crane
(fd, style=0)[source]¶ Returns the loss coefficient for a foot valve of either poppet disc (style = 0) or hingeddisk (style = 1) as shown in [1]. Both valves are specified include the loss of the attached strainer.
\[K = K_1 = K_2 = N\cdot f_d\]For style 0 (poppet disk), N = 420; for style 1 (hinged disk), N = 75.
Parameters:  fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
Either 0 (poppet disk foot valve) or 1 (hinged disk foot valve) []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_foot_valve_Crane(0.015, style=0) 6.3

fluids.fittings.
K_butterfly_valve_Crane
(D, fd, style=0)[source]¶ Returns the loss coefficient for a butterfly valve as shown in [1]. Three different types are supported; Centric (style = 0), double offset (style = 1), and triple offset (style = 2).
\[K = N\cdot f_d\]N is obtained from the following table:
Size range Centric Double offset Triple offset 2”  8” 45 74 218 10”  14” 35 52 96 16”  24” 25 43 55 The actual change of coefficients happen at <= 9” and <= 15”.
Parameters:  D : float
Diameter of the pipe section the valve in mounted in; the same as the line size [m]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
Either 0 (centric), 1 (double offset), or 2 (triple offset) []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_butterfly_valve_Crane(.01, .016, style=2) 3.488

fluids.fittings.
K_plug_valve_Crane
(D1, D2, angle, fd, style=0)[source]¶ Returns the loss coefficient for a plug valve or cock valve as shown in [1].
If β = 1:
\[K = K_1 = K_2 = Nf_d\]Otherwise:
\[K_2 = \frac{K + 0.5\sqrt{\sin\frac{\theta}{2}}(1\beta^2) + (1\beta^2)^2}{\beta^4}\]Three types of plug valves are supported. For straightthrough plug valves (style = 0), N = 18. For 3way, flow straight through (style = 1) plug valves, N = 30. For 3way, flow 90° valves (style = 2) N = 90.
Parameters:  D1 : float
Diameter of the valve plug bore (must be equal to or smaller than D2), [m]
 D2 : float
Diameter of the pipe attached to the valve, [m]
 angle : float
Angle formed by the reducer in the valve, [degrees]
 fd : float
Darcy friction factor calculated for the actual pipe flow in clean steel (roughness = 0.0018 inch) in the fully developed turbulent region []
 style : int, optional
Either 0 (straightthrough), 1 (3way, flow straightthrough), or 2 (3way, flow 90°) []
Returns:  K : float
Loss coefficient with respect to the pipe inside diameter []
Notes
This method is not valid in the laminar regime and the pressure drop will be underestimated in those conditions.
References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> K_plug_valve_Crane(.01, .02, 50, .025) 20.100545785228675

fluids.fittings.
K_branch_converging_Crane
(D_run, D_branch, Q_run, Q_branch, angle=90)[source]¶ Returns the loss coefficient for the branch of a converging tee or wye according to the Crane method [1].
\[ \begin{align}\begin{aligned}K_{branch} = C\left[1 + D\left(\frac{Q_{branch}}{Q_{comb}\cdot \beta_{branch}^2}\right)^2  E\left(1  \frac{Q_{branch}}{Q_{comb}} \right)^2  \frac{F}{\beta_{branch}^2} \left(\frac{Q_{branch}} {Q_{comb}}\right)^2\right]\\\beta_{branch} = \frac{D_{branch}}{D_{comb}}\end{aligned}\end{align} \]In the above equation, D = 1, E = 2. See the notes for definitions of F and C.
Parameters:  D_run : float
Diameter of the straightthrough inlet portion of the tee or wye [m]
 D_branch : float
Diameter of the pipe attached at an angle to the straightthrough, [m]
 Q_run : float
Volumetric flow rate in the straightthrough inlet of the tee or wye, [m^3/s]
 Q_branch : float
Volumetric flow rate in the pipe attached at an angle to the straight through, [m^3/s]
 angle : float, optional
Angle the branch makes with the straightthrough (tee=90, wye<90) [degrees]
Returns:  K : float
Loss coefficient of branch with respect to the velocity and inside diameter of the combined flow outlet []
Notes
F is linearly interpolated from the table of angles below. There is no cutoff to prevent angles from being larger or smaller than 30 or 90 degrees.
Angle [°] 30 1.74 45 1.41 60 1 90 0 If \(\beta_{branch}^2 \le 0.35\), C = 1
If \(\beta_{branch}^2 > 0.35\) and \(Q_{branch}/Q_{comb} > 0.4\), C = 0.55.
If neither of the above conditions are met:
\[C = 0.9\left(1  \frac{Q_{branch}}{Q_{comb}}\right)\]Note that there is an error in the text of [1]; the errata can be obtained here: http://www.flowoffluids.com/publications/tp410errata.aspx
References
[1] (1, 2, 3, 4) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
Example 735 of [1]. A DN100 schedule 40 tee has 1135 liters/minute of water passing through the straight leg, and 380 liters/minute of water converging with it through a 90° branch. Calculate the loss coefficient in the branch. The calculated value there is 0.04026.
>>> K_branch_converging_Crane(0.1023, 0.1023, 0.018917, 0.00633) 0.04044108513625682

fluids.fittings.
K_run_converging_Crane
(D_run, D_branch, Q_run, Q_branch, angle=90)[source]¶ Returns the loss coefficient for the run of a converging tee or wye according to the Crane method [1].
\[ \begin{align}\begin{aligned}K_{branch} = C\left[1 + D\left(\frac{Q_{branch}}{Q_{comb}\cdot \beta_{branch}^2}\right)^2  E\left(1  \frac{Q_{branch}}{Q_{comb}} \right)^2  \frac{F}{\beta_{branch}^2} \left(\frac{Q_{branch}} {Q_{comb}}\right)^2\right]\\\beta_{branch} = \frac{D_{branch}}{D_{comb}}\end{aligned}\end{align} \]In the above equation, C=1, D=0, E=1. See the notes for definitions of F and also the special case of 90°.
Parameters:  D_run : float
Diameter of the straightthrough inlet portion of the tee or wye [m]
 D_branch : float
Diameter of the pipe attached at an angle to the straightthrough, [m]
 Q_run : float
Volumetric flow rate in the straightthrough inlet of the tee or wye, [m^3/s]
 Q_branch : float
Volumetric flow rate in the pipe attached at an angle to the straight through, [m^3/s]
 angle : float, optional
Angle the branch makes with the straightthrough (tee=90, wye<90) [degrees]
Returns:  K : float
Loss coefficient of run with respect to the velocity and inside diameter of the combined flow outlet []
Notes
F is linearly interpolated from the table of angles below. There is no cutoff to prevent angles from being larger or smaller than 30 or 60 degrees. The switch to the special 90° happens at 75°.
Angle [°] 30 1.74 45 1.41 60 1 For the special case of 90°, the formula used is as follows.
\[K_{run} = 1.55\left(\frac{Q_{branch}}{Q_{comb}} \right)  \left(\frac{Q_{branch}}{Q_{comb}}\right)^2\]References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
Example 735 of [1]. A DN100 schedule 40 tee has 1135 liters/minute of water passing through the straight leg, and 380 liters/minute of water converging with it through a 90° branch. Calculate the loss coefficient in the run. The calculated value there is 0.03258.
>>> K_run_converging_Crane(0.1023, 0.1023, 0.018917, 0.00633) 0.32575847854551254

fluids.fittings.
K_branch_diverging_Crane
(D_run, D_branch, Q_run, Q_branch, angle=90)[source]¶ Returns the loss coefficient for the branch of a diverging tee or wye according to the Crane method [1].
\[ \begin{align}\begin{aligned}K_{branch} = G\left[1 + H\left(\frac{Q_{branch}}{Q_{comb} \beta_{branch}^2}\right)^2  J\left(\frac{Q_{branch}}{Q_{comb} \beta_{branch}^2}\right)\cos\theta\right]\\\beta_{branch} = \frac{D_{branch}}{D_{comb}}\end{aligned}\end{align} \]See the notes for definitions of H, J, and G.
Parameters:  D_run : float
Diameter of the straightthrough inlet portion of the tee or wye [m]
 D_branch : float
Diameter of the pipe attached at an angle to the straightthrough, [m]
 Q_run : float
Volumetric flow rate in the straightthrough outlet of the tee or wye, [m^3/s]
 Q_branch : float
Volumetric flow rate in the pipe attached at an angle to the straight through, [m^3/s]
 angle : float, optional
Angle the branch makes with the straightthrough (tee=90, wye<90) [degrees]
Returns:  K : float
Loss coefficient of branch with respect to the velocity and inside diameter of the combined flow inlet []
Notes
If \(\beta_{branch} = 1, \theta = 90^\circ\), H = 0.3 and J = 0. Otherwise H = 1 and J = 2.
G is determined according to the following pseudocode:
if angle < 75: if beta2 <= 0.35: if Q_ratio <= 0.4: G = 1.1  0.7*Q_ratio else: G = 0.85 else: if Q_ratio <= 0.6: G = 1.0  0.6*Q_ratio else: G = 0.6 else: if beta2 <= 2/3.: G = 1 else: G = 1 + 0.3*Q_ratio*Q_ratio
Note that there are several errors in the text of [1]; the errata can be obtained here: http://www.flowoffluids.com/publications/tp410errata.aspx
References
[1] (1, 2, 3, 4) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
Example 736 of [1]. A DN150 schedule 80 wye has 1515 liters/minute of water exiting the straight leg, and 950 liters/minute of water exiting it through a 45° branch. Calculate the loss coefficient in the branch. The calculated value there is 0.4640.
>>> K_branch_diverging_Crane(0.146, 0.146, 0.02525, 0.01583, angle=45) 0.4639895627496694

fluids.fittings.
K_run_diverging_Crane
(D_run, D_branch, Q_run, Q_branch, angle=90)[source]¶ Returns the loss coefficient for the run of a converging tee or wye according to the Crane method [1].
\[ \begin{align}\begin{aligned}K_{run} = M \left(\frac{Q_{branch}}{Q_{comb}}\right)^2\\\beta_{branch} = \frac{D_{branch}}{D_{comb}}\end{aligned}\end{align} \]See the notes for the definition of M.
Parameters:  D_run : float
Diameter of the straightthrough inlet portion of the tee or wye [m]
 D_branch : float
Diameter of the pipe attached at an angle to the straightthrough, [m]
 Q_run : float
Volumetric flow rate in the straightthrough outlet of the tee or wye, [m^3/s]
 Q_branch : float
Volumetric flow rate in the pipe attached at an angle to the straight through, [m^3/s]
 angle : float, optional
Angle the branch makes with the straightthrough (tee=90, wye<90) [degrees]
Returns:  K : float
Loss coefficient of run with respect to the velocity and inside diameter of the combined flow inlet []
Notes
M is calculated according to the following pseudocode:
if beta*beta <= 0.4: M = 0.4 elif Q_branch/Q_comb <= 0.5: M = 2*(2*Q_branch/Q_comb  1) else: M = 0.3*(2*Q_branch/Q_comb  1)
References
[1] (1, 2, 3) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
Example 736 of [1]. A DN150 schedule 80 wye has 1515 liters/minute of water exiting the straight leg, and 950 liters/minute of water exiting it through a 45° branch. Calculate the loss coefficient in the branch. The calculated value there is 0.06809.
>>> K_run_diverging_Crane(0.146, 0.146, 0.02525, 0.01583, angle=45) 0.06810067607153049

fluids.fittings.
v_lift_valve_Crane
(rho, D1=None, D2=None, style='swing check angled')[source]¶ Calculates the approximate minimum velocity required to lift the disk or other controlling element of a check valve to a fully open, stable, position according to the Crane method [1].
\[ \begin{align}\begin{aligned}v_{min} = N\cdot \text{m/s} \cdot \sqrt{\frac{\text{kg/m}^3}{\rho}}\\v_{min} = N\beta^2 \cdot \text{m/s} \cdot \sqrt{\frac{\text{kg/m}^3}{\rho}}\end{aligned}\end{align} \]See the notes for the definition of values of N and which check valves use which formulas.
Parameters:  rho : float
Density of the fluid [kg/m^3]
 D1 : float, optional
Diameter of the valve bore (must be equal to or smaller than D2), [m]
 D2 : float, optional
Diameter of the pipe attached to the valve, [m]
 style : str
The type of valve; one of [‘swing check angled’, ‘swing check straight’, ‘swing check UL’, ‘lift check straight’, ‘lift check angled’, ‘tilting check 5°’, ‘tilting check 15°’, ‘stop check globe 1’, ‘stop check angle 1’, ‘stop check globe 2’, ‘stop check angle 2’, ‘stop check globe 3’, ‘stop check angle 3’, ‘foot valve poppet disc’, ‘foot valve hinged disc’], []
Returns:  v_min : float
Approximate minimum velocity required to keep the disc fully lifted, preventing chattering and wear [m/s]
Notes
This equation is not dimensionless.
Name/string N Full ‘swing check angled’ 45 No ‘swing check straight’ 75 No ‘swing check UL’ 120 No ‘lift check straight’ 50 Yes ‘lift check angled’ 170 Yes ‘tilting check 5°’ 100 No ‘tilting check 15°’ 40 No ‘stop check globe 1’ 70 Yes ‘stop check angle 1’ 95 Yes ‘stop check globe 2’ 75 Yes ‘stop check angle 2’ 75 Yes ‘stop check globe 3’ 170 Yes ‘stop check angle 3’ 170 Yes ‘foot valve poppet disc’ 20 No ‘foot valve hinged disc’ 45 No References
[1] (1, 2) Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane, 2009. Examples
>>> v_lift_valve_Crane(rho=998.2, D1=0.0627, D2=0.0779, style='lift check straight') 1.0252301935349286