Pressure drop across a valve in hydraulics

[Mr bboy]

Hello,
I read something about the pressure drop across a valve and it was specified this is a singular pressure drop equivalent to K*U²/g (Borda formula). My question is, can we used the Bernouilli formula for a permanant incompressible flow to determine the flow rate function of the pressure drop. With the introduction of a coefficient C to take into account the energy loss through the valve. The flow rate expression is Q= S*C*A(V)*(2dP/rho)^0.5 with S the surface, A(V) a coefficient function of the velocity. It appear that a valve is similar to a diaphragm used in the experimentations. Are these expressions similar ?

Thank you for your help !

 

[JBA]

Ironically, either equation can be applicable as long as there is an experimentally established C coefficient for the valve based upon the differential between the measured flow test vs the specific selected equation results. In the relief valve industry the Bernoulli formula is used for the calculated estimate of the flow for a fully opened valve utilizing the orifice diameter or the annular flow area between the valve orifice and the valve seat. At the same time, the coefficient will significantly vary based upon the combination of the valve nozzle design, the lift of the valve and the overall internal valve body configuration starting at the inlet connection and ending at the valve outlet connection . As a result, for an accurate result of the flow and pressure loss through a valve a coefficient curve based upon flow vs lift or opening position is required.

 

[Mr bboy]

Thank you JBA for the answer. I have an additional question about your last comment:

"a coefficient curve based upon flow vs lift or opening position is required." If i understand well the C coefficient will change with the ratio of the valve. Do you have an idea why in the theory for the proportional valves we define a constant C coefficient (as you mentioned the flow will be more or less turbulent with the position of the valve)?

 

[JBA]

This probably has to do with the specific operating cycle of the valve in focus. In modulating valves, the valve often does not fully open during a relieving cycle; so, the critical flow area in the valve transitions from an annular type orifice between the flat disc face and the top of the valve seat to a full flowing orifice when the valve is in full lift. Also, flow turbulence in the right angle configuration discharge region of the valve body can have an effect on the total pressure drop of a liquid, or subsonic gas, valve.

Alternatively, a type of liquid control valve that can operate with a single coefficient are flow choke valves that are designed with a round orifice and a pointed conical regulating stem. In these valves, the effective annular flowing orifice form between the seat and cone changes very linearly as the cone is withdrawn and the cone is never fully withdrawn from the orifice. These valves also generally have straight through discharge body configuration that does not significantly effect the pressure drop in the valve flow stream. Even in these valves, in some cases, the controlling conical stem end is contoured based upon flow tests to compensate for any potential variations of actual coefficient during the opening stroke of the valve.

Another case where a constant coefficient can be applied across the valve's opening is diaphragm type modulating instrument control valves where the lift during operation is very limited so that the annular orifice formed between the flat disc face and the top of the valve seat is very small relative to the diameter of the inlet orifice and remains the critical flow restriction point throughout the valve's lift range.

So, ultimately it comes down to the overall function of the valve and its body inlet and outlet configurations effect, if significant, because in liquid flow, just as in subsonic gas flow, all elements along the flow path can have an ultimate effect on the flowing pressure drop through the valve.