Flow and Loss Coefficients 3

[TreeEng]

Can someone explain the difference between Cv and Cd? Also, is there an equation to convert between Cd and Cv? I have a reference to this equation for finding the Cv of a valve:

Cv ~ 38*A*Cd

A=cross-sectional area

Cd was assumed to be 0.6. I do not know where this equation comes from or if Cd=0.6 is reasonable. Is anyone else familiar with this?

Any help is much appreciated.

 

[TD2K]

I haven't seen this link before between the two, you would have to get some information on various valves and compare them. What does the A apply to? I would assume it's the port area.

Cd is the discharge coefficient for an orifice and is essentially a factor for how close your orifice/nozzle comes to a perfectly smooth nozzle.

Cv for a valve is an indication of its capacity. For water, a Cv of 1 means it will flow 1 gal/min for a dp of 1 psi (Q = Cv (dP/SG)^.5)

 

[Tremolo]

TreeEng,

This topic has come up for discussion previoulsy. See thread408-46925


In that thread, I responded as follows:

I often covert between Cv and Cd. Here's how to do it. I have included a conversion factor in case you are working in gpm and psi.

First, the governing equations for volumetric flow, Q, in gpm:

Q = Cd*A*sqrt(2*dP/rho)*F

where,

Cd is the discharge coefficient
A is the flow area
sqrt is the mathematical symbol for square root
dP is the pressure drop
rho is the fluid density
F is the conversion factor to get gpm assuming the pressure is in psi, area in ft^2 and density in lb/ft^3; note that F is outside of the sqrt. F = sqrt(32.2*144)*7.48*60 = 30561.

Given a valve flow coefficient, Cv, the volumetric flow rate is,

Q = Cv*sqrt(dP)

Q is in gpm
dP is in psi
Cv is in gpm/sqrt(psi)

Setting the two equations equal to each other and solving for Cd yields,

Cd = Cv*sqrt(rho/2)/F/A


If using gpm and psi, then F = 30561.

If SI units are used, for which P is in Pa, flow rate is m^3/s and Cv is (m^3/s)/sqrt(Pa), the conversion factor is F=1.


TreeEng,

To answer your basic question, Cv and Cd both express the hydraulic resistance of a pipeline component such as a valve, orifice, or nozzle. The Cv is typically used for valves and is avaiable from manufacturers. As pointed out by TD2K, Cd is typically used to indicate variations from the ideal nozzle or orifice.

As for your equation, Cv ~ 38*A*Cd, I do not think that is valid. I cannot get there from the equations I laid out above.

 

[BRIS]

All depends on the units - cv is unit dependent and is usually in FPS units, whereas cd is non-dimensional.

Cv = k x A x cd

Where k is a constant dependent on the units used.

my quick calc for water in SI unts gives me

Cv = 25909 x A x cd

where Cv = 1.156 x Q x (G/dp)^0.5

Q = m3/hour
G = specific gravity water
dp = presure drop in bar.

But back to the question. cd = 0.6 is reasonable for an orifice where the orifice diameter is less than about 55% of the pipe diameter. It is not reasonable for a valve. For a valve Cd (fully open) will depend on the type of valve.

 

[4carats]

TreeEng

Regarding the equations that you posted:

Cv ~ 38*A*Cd

A=cross-sectional area

please see Crane Technical Publication 410.

In Crane, you will find that Cv = 29.9 d^2 /sqrt(K), where
(pi)d^2/4 = A, i.e. the effective cross-sectional area.

Therefore Cv/A = 38/sqrt(K).

Hence, 1/sqrt(K) = Cd, where
K is the loss coefficient of the physical cross-sectional area.

Substituting and solving, you will get

Cv ~ 38*A*Cd

A=cross-sectional area

I hope this helps.

4carats