Mechanical enery equation to valve equation

[Fingon]

Hi

I’m writing my bachelor thesis about valves, and was wondering if anyone could help me with the following derivation:
I need to show the algebraic link between the mechanical energy-equation and the ”valve equation” that is Cv=Q * [Square](Sg/[Delta]p). This can also be called the flow coefficient-equation.

Everything in field units (american units)

All help will be appreciated a lot!

 

[Andrew Mason]

Hi

I’m writing my bachelor thesis about valves, and was wondering if anyone could help me with the following derivation:
I need to show the algebraic link between the mechanical energy-equation and the ”valve equation” that is Cv=Q * [Square](Sg/[Delta]p). This can also be called the flow coefficient-equation.

Everything in field units (american units)

All help will be appreciated a lot!

Pressure is energy / unit volume so the $\Delta P = Q^2\rho/C_v$ expresses an energy loss per unit volume.

AM

 

[quark]

Derive it from Bernoulli's. As the length of the valve is generally too small, you can neglect difference in elevation (if any) and also it is a safe assumption to consider constant velocity. The pressure drop across the valve then becomes a function of velocity. Express frictional resistance in terms of velocity and equate it to pressure drop.