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 + (\lambda-1)^2\\\lambda = 1 + 0.622(1-0.215\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] 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 + (\lambda-1)^2\\\lambda = 1 + 0.622\left(1 - 0.30\sqrt{\frac{r}{d_2}} - 0.70\frac{r}{d_2}\right)^4 (1-0.215\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] rc : float Radius of curvature of the contraction, [m] 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 + (\lambda-1)^2\\\lambda = 1 + 0.622(\alpha/180)^{0.8}(1-0.215\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] fd : float Darcy friction factor [-] l : float Length of the contraction, optional [m] angle : float Angle of contraction, optional [degrees] 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 + (\lambda-1)^2\\\lambda = 1 + 0.622\left[1+C_B\left(\left(\frac{\alpha}{180} \right)^{0.8}-1\right)\right](1-0.215\beta^2-0.785\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] 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] 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:

$K_1 = \left\{1.366\sin\left[\frac{2\pi(\alpha-15^\circ)}{180}\right]^{0.5} - 0.170 - 3.28(0.0625-\beta^4)\sqrt{\frac{\alpha-20^\circ}{40^\circ}}\right\} (1-\beta^2)^2 + \frac{f(1-\beta^4)}{8\sin(\alpha/2)}$

For 20 to 60 degrees, beta >= 0.5:

$K_1 = \left\{1.366\sin\left[\frac{2\pi(\alpha-15^\circ)}{180}\right]^{0.5} - 0.170 \right\}(1-\beta^2)^2 + \frac{f(1-\beta^4)}{8\sin(\alpha/2)}$

For 60 to 180 degrees, beta < 0.5:

$K_1 = \left[1.205 - 3.28(0.0625-\beta^4)-12.8\beta^6\sqrt{\frac {\alpha-60^\circ}{120^\circ}}\right](1-\beta^2)^2$

For 60 to 180 degrees, beta >= 0.5:

$K_1 = \left[1.205 - 0.20\sqrt{\frac{\alpha-60^\circ}{120^\circ}} \right](1-\beta^2)^2$
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 [-] 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 [-] 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(1.43-1.3\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] 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_1-d_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 [-] 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] 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] 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 + (\lambda-1)^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] 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 + (\lambda-1)^2\\\lambda = 1 + 0.622\left[1-1.5C_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] 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 [-] 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 single-joint 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] 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 constant-pitch 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 [-] 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 constant-pitch 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 [-] 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] 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): 127,129-130.

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 constant-K 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 [-] 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 2-K 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] 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 60534-2-1. 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 pound-force per square inch.

The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.

References

 [R411440] ISA-75.01.01-2007 (60534-2-1 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] 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 60534-2-1. 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 pound-force per square inch.

The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.

References

 [R412441] ISA-75.01.01-2007 (60534-2-1 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] 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 5-40°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 IAPWS-95; 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] ISA-75.01.01-2007 (60534-2-1 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] 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 5-40°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 IAPWS-95; 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] ISA-75.01.01-2007 (60534-2-1 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] 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] ISA-75.01.01-2007 (60534-2-1 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] 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 pound-force per square inch.

The exact conversion coefficient between Kv to Cv is 1.1560992283536566; it is rounded in the formula above.

References

 [R416445] ISA-75.01.01-2007 (60534-2-1 Mod) Draft

Examples

>>> K_to_Cv(16, .015)
2.601223263795727