Fittings pressure drop (fluids.fittings)¶

fluids.fittings.
contraction_sharp
(Di1, Di2)[source]¶ Returns loss coefficient for any sharp edged pipe contraction as shown in [R387416].
\[ \begin{align}\begin{aligned}K = 0.0696(1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622(10.215\beta^2  0.785\beta^5)\\\beta = d_2/d_1\end{aligned}\end{align} \]Parameters: Di1 : float
Inside diameter of original pipe, [m]
Di2 : float
Inside diameter of following pipe, [m]
Returns: K : float
Loss coefficient []
Notes
A value of 0.506 or simply 0.5 is often used.
References
[R387416] (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 [R388417].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  0.569\frac{r}{d_2}\right)\left(1\sqrt{\frac{r} {d_2}}\beta\right)(1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left(1  0.30\sqrt{\frac{r}{d_2}}  0.70\frac{r}{d_2}\right)^4 (10.215\beta^20.785\beta^5)\\\beta = d_2/d_1\end{aligned}\end{align} \]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 []
Notes
Rounding radius larger than 0.14Di2 prevents flow separation from the wall. Further increase in rounding radius continues to reduce loss coefficient.
References
[R388417] (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 [R389418].
\[ \begin{align}\begin{aligned}K = 0.0696[1+C_B(\sin(\alpha/2)1)](1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622(\alpha/180)^{0.8}(10.215\beta^20.785\beta^5)\\\beta = d_2/d_1\end{aligned}\end{align} \]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 []
Notes
Cheap and has substantial impact on pressure drop.
References
[R389418] (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 [R390419].
\[ \begin{align}\begin{aligned}K = 0.0696[1+C_B(\sin(\alpha/2)1)](1\beta^5)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left[1+C_B\left(\left(\frac{\alpha}{180} \right)^{0.8}1\right)\right](10.215\beta^20.785\beta^5)\\C_B = \frac{l}{d_2}\frac{2\beta\tan(\alpha/2)}{1\beta}\\\beta = d_2/d_1\end{aligned}\end{align} \]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 []
References
[R390419] (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 [R391420] 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
[R391420] (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 [R392421]. 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
[R392421] (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 [R393422]. 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
[R393422] (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 [R394423].
\[ \begin{align}\begin{aligned}K_1 = \phi(1.431.3\beta^2)(1\beta^2)^2\\\phi = 1.01  0.624\frac{l}{d_1} + 0.30\left(\frac{l}{d_1}\right)^2  0.074\left(\frac{l}{d_1}\right)^3 + 0.0070\left(\frac{l}{d_1}\right)^4\end{aligned}\end{align} \]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
[R394423] (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
[R395424] 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 [R396425].
\[K = 0.57\]Returns: K : float
Loss coefficient []
Notes
Other values used have been 0.5.
References
[R396425] (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 [R397426].
\[K = 1.12  22\frac{t}{d} + 216\left(\frac{t}{d}\right)^2 + 80\left(\frac{t}{d}\right)^3\]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 [R397426].
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
[R397426] (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 [R398427].
\[K = 0.57 + 0.30\cos(\theta) + 0.20\cos(\theta)^2\]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
[R398427] (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 [R399428].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  0.569\frac{r}{d}\right)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left(1  0.30\sqrt{\frac{r}{d}}  0.70\frac{r}{d}\right)^4\end{aligned}\end{align} \]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
[R399428] (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 [R400429].
\[ \begin{align}\begin{aligned}K = 0.0696\left(1  C_b\frac{l}{d}\right)\lambda^2 + (\lambda1)^2\\\lambda = 1 + 0.622\left[11.5C_b\left(\frac{l}{d} \right)^{\frac{1(l/d)^{1/4}}{2}}\right]\\C_b = \left(1  \frac{\theta}{90}\right)\left(\frac{\theta}{90} \right)^{\frac{1}{l+l/d}}\end{aligned}\end{align} \]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
[R400429] (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.
exit_normal
()[source]¶ Returns loss coefficient for any exit to a pipe as shown in [R401430] 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
[R401430] (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 [R402431].
\[K = f\alpha\frac{r}{d} + (0.10 + 2.4f)\sin(\alpha/2) + \frac{6.6f(\sqrt{\sin(\alpha/2)}+\sin(\alpha/2))} {(r/d)^{\frac{4\alpha}{\pi}}}\]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.
References
[R402431] (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 [R403432].
\[K = 0.42\sin(\alpha/2) + 2.56\sin^3(\alpha/2)\]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
[R403432] (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 [R404433]. 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
[R404433] (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 [R405434]. 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
[R405434] (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 [R406435]. 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
[R406435] (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. [R407435] 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 [R408437]. 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
[R408437] (1, 2) Hooper, W. B., “The 2K Method Predicts Head Losses in Pipe Fittings,” Chem. Eng., p. 97, Aug. 24 (1981). [R409437] Hooper, William B. “Calculate Head Loss Caused by Change in Pipe Size.” Chemical Engineering 95, no. 16 (November 7, 1988): 89. [R410437] 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
[R411440] 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
[R412441] 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
[R413442] 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
[R414443] 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
[R415444] 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
[R416445] ISA75.01.012007 (6053421 Mod) Draft Examples
>>> K_to_Cv(16, .015) 2.601223263795727