Flow rate through a valve

[firefastball]

From internet source " Rate of flow through a valve depends upon pressure drop. The most common method of presenting this information is by valve coefficient of flow. The valve coefficient of flow represents the flow of water in gallons per minute with a 1 PSIG pressure drop through the valve. The higher the valve coefficient the greater the flow and the better the control charateristics. Formula : Volume flow rate = Flow coefficient x Square root( pressure drop/ valve coefficient)"

According to the reliable source, volume flow rate is dependent on drop in pressure and valve coefficient.

What iam puzzled is, isnt volume flow rate = velocity x flow area? Volume flow rate should be dependent on velocity right? From velocity profile across valve, velocity reaches a maximum when the flow area across valve is minimum. However, when fluid exits valve, flow area increases and velocity is almost the same as velocity of fluid into valve. Since inlet velocity and outlet velocity is same, why does volume flow rate drop across a valve when flow rate = velocity x area of pipe (inlet and outlet pipe area same). I can't seem to understand fluid law of continuity across a valve opening.

Can someone explain to me from a physics point of view. Thanks

 

[katmar]

For a given valve opening, the volumetric flow of an incompressible fluid is the same through all planes perpendicular to the direction of flow. Local velocities whill change with changes in cross sectional area to maintain constant volumetric flow.

A useful analogy is a traffic jam. Imagine a situation where a 5 lane highway is reduced to one lane. You travel very slowly in the 5 lanes approaching the restriction, but as soon as you are into the single lane you speed up significantly. At any point in the traffic jam the "volumetric flow" in cars per minute remains the same.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[e43u8]

firefastball,

If you are discussing about incompressible flow, katmar well mentioned the reason by which you might understand why the volumetric flow rate maintains constant while the fluid is passing through a valve...

But if you meant compressible flow, then the volumetric flow rate is decreasing while the fluid is passing through a valve because basically Volumetric flow=Mass flow/Density and with fixed mass flow due to lower pressure at valve exit, the fluid density will be reduced and there would be an increment in volumetric flow at valve downstream...

 

[bimr]

The fluid law of continuity across a valve opening is demonstrated by the Bernoulli equation.

The total energy is the sum of the pressure and kinetic energy. As the fluid accelerates across the valve, the pressure decreases and the kinetic energy increases. Pressure energy (P) is changed to kinetic energy (V2/2g) with the increase in velocity and then back to pressure energy(P) after the valve. The total energy is the same except for the head loss across the valve.

 

[firefastball]

Let say that water before a control valve is at 10 bar with flow 100 m3/s. The control valve is set at 50% opening. There will be a pressure drop on the other side of the pipe, say 5 bar. Does the flow remains the same or it decrease with pressure?

 

[LittleInch]

Re-reading your original post again and from the replies given, it seems to me that you are not thinking this through correctly.

The key is that in steady state flow, liquid mass flow rate (volumetric flow rate) is the same at all places along the pipe including the valve. When you change the valve opening the pressure drop across the valve changes, assuming the inlet pressure stays the same. This reduces flow rate at ALL points in that system.

For liquid systems, it is the pressure drop from one side of the valve to the other that is the key factor. You could have 100 bar one side and 95 the other side or 10 bar one side and 5 bar the other side and with EVERYTHING ELSE being the same then you would get the same flowrate through the valve. Gas is different as pressure affects the density and hence mass, but liquids will normally obey this rule.

Hence you need to understand your system to know how much changing the opening of a valve affects the flowrate. Note also that the pressure drop of an open control valve only occurs when there is flow. Only when you have a regulator will this change.

Many times you can use electricity flow as an analogy if this is easier. Your control valve is a variable resistor. Only when you have current flow will you get a voltage drop.

BTW 100m3/sec is a very big flow....

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[bimr]

The flow through the pipe is a function of the pressure pushing it.

Since you are losing energy (pressure) with the pressure drop across the valve, the flow decreases with the pressure drop across the valve.

C_v = F *sqrt(SG\Delta P)

where:
C_v = Flow coefficient or flow capacity rating of valve.
F = Rate of flow (US gallons per minute).
SG = Specific gravity of fluid (Water = 1).
ΔP = Pressure drop across valve (psi).


See Figure 4 in the attachment.