# How to calculate the flow coefficient of a valve

In the past couple of months I have seen two examples of customers interested in the calculation of the flow coefficient of a valve. Known as Cv, the flow coefficient is a relative value that allows us to compare the efficiency of different valves regardless of their size or type.

Before we see how to simulate this using SolidWorks Flow Simulation it is important to note that the calculation of Cv differs for gases, liquids, and even steam and can change depending on the pressure drop across the valve. For a list of the relevant equations look up https://www.engineeringtoolbox.com/flow-coefficients-d_277.html.

However in essence the equations follow the same basic principle,

where q is the flow rate, SG is the specific gravity of the fluid, and dp is the pressure drop across the valve.

So to model this in Flow Simulation, simply define the pressure drop across the valve with explicit inlet and outlet pressure conditions and measure the flow rate.

For example, you might apply an environmental pressure of 16 bar at the inlet, a static pressure of 15 bar at the outlet, and measure the flow rate at the outlet.

Also, by defining the inlet and outlet pressures and flow rate as goals, it is pretty easy to set up an equation goal that will automatically calculate the Cv value for you.

Here is the equation goal I used for air flowing through a valve with a non-critical pressure drop. Whilst it looks daunting, it is actually just referring to a whole load of other goals picked directly from the list in the flow simulation analysis tree so it’s not that difficult.

I want to finish by mentioning a couple of points. You have to be very careful to use consistent units when calculating the flow coefficient, and the Imperial system is common. Also keep an eye on definitions, for example, the term for q that I used is actually required in ‘standard cubic feet per minute’, which is not the basic cfm calculated by flow simulation. Here I have factored it to standardised conditions of temperature and pressure in the first few terms.

q = ({Average Outlet Pressure, Pa}/101325)*(273.15/{Average Temperature of Fluid, K})*{Outlet Volume Flow Rate, cfm}

And finally it is good practice to calculate the Cv value for two or three different pressure drops and take the average, just as you would with a physical test.

#### Matthew West

SolidWorks alumnus. I like plate reverb, Rat pedals, Thai curry, New Weird fiction, my kids, Vespas, Jazzmasters, my wife & Raiders of the Lost Ark. Not necessarily in that order.