The valve flow coefficient is an essential measurement that helps you calculate how much fluid can pass through a valve. The valve flow coefficient (Cv) can measure the rate at which any gas or liquid can pass through a valve.

In this article, we’ll go into detail about what a valve flow coefficient is as well as how to calculate it. We’ll give you a step-by-step breakdown of how to perform these calculations.

Finally, we’ll give you a few examples you can work on by yourself to see if you have your valve flow coefficient calculations down pat.

What Is a Valve Flow Coefficient?

The valve flow coefficient is a measurement that pipefitters, engineers, and manufacturers use to find the right-sized valves for the amount of fluid that will pass through them.

Put simply; the Cv helps workers choose the right size valve so all fluids can pass through at the desired pressure.

The valve flow coefficient is defined as “the number of U.S. gallons per minute of water that will pass through a given orifice area at a pressure drop of 1 pound-force per square inch (PSI).”

Although water is the base measurement, you can calculate the valve flow coefficient for gasses or other liquids using the same principle.

Let’s give you an example to help you understand this principle. If a particular valve has a valve flow coefficient of 1.00, it will allow 1 gallon per minute (GPM) of water through the valve with a pressure drop of 1 PSI.

Since we are using water, it has a specific gravity (G) of 1. We’ll get into specific gravity during the calculations part of this article.

Let’s change up some variables. You have the same pressure drop of 1 PSI, and since we’re using water, the specific gravity is the same as before. But now, you’d like your valve to allow 2 GPM through. In this case, you’d need a different valve with a valve flow coefficient of 2.0.

So as you can see, the valve flow coefficient is an essential calculation for anyone who works with pipes.

What is the Cv Equation?

To calculate the valve flow coefficient, you’d use the formula:

Cv = Q√(SG / ΔP

Where:

• Cv = Valve flow coefficient
• Q = Flow rate (GPM)
• SG = Specific gravity (dimensionless)
• ΔP = Pressure drop (PSI)

Now let’s define all the different variables we’ll need to use for the calculations.

Valve Flow Coefficient Variables

When calculating the valve flow coefficient, you need to know specific aspects about the fluid, the valve, and how much fluid you want to pass through the valve. Let’s go through the different variables before explaining how to calculate the valve flow coefficient.

Specific Gravity

Specific gravity (SG) is a ratio of a fluid’s weight to the weight of water at 4°C (39.2°F). 

The most obvious example of this is water itself. Water has a specific gravity of 1.00 because it is a ratio of itself. A more dense fluid would have a higher ratio, while a less dense fluid would have a lower ratio.

As an example, let’s examine the specific gravity of hydraulic oil. Hydraulic oil weighs 0.8 grams/milliliter. Water, as we know, weighs 1 gram/milliliter.

Therefore, hydraulic oil has a specific gravity of 0.8, much lower than water. If you can find the weight of any fluid in grams/milliliter, you can easily calculate the fluid’s specific gravity.

Rate of Flow

The rate of flow (Q) is the variable that represents how much of the fluid is passing through the valve at a given time.

We usually represent this number in GPM (Gallons Per Minute). To calculate the rate of flow, you need to know the volume (V) and the time (t) it takes for that volume to pass through the valve.

To find Q, divide V by t and convert to gallons per minute (GPM). So if we have a 1-gallon volume of water and it takes 10 seconds to run through the valve, it has a flow rate of 6 GPM. Q = (1 gallon / 10 seconds) × 60 seconds/minute = 6 GPM

As another example, if we have 100 gallons of water and it takes 15 minutes to run through the valve, the rate of flow would be 6.67 GPM. Q = 100 gallons / 15 minutes ≈ 6.67 GPM

Pressure Drop

Pressure drop (ΔP), measured in pounds per square inch (PSI), is the difference in pressure between two points in a fluid system. This difference is caused by the resistance to flow in the pipe, fittings, and the valve itself. It is the most complex variable in this equation to calculate, which is why it is recommended to use charts or specialized software to figure out the pressure drop for specific types of pipes.

If you don’t use charts, you can always use the Darcy-Weisbach Equation below to determine your pressure drop. If this looks too daunting to figure out, those charts are going to be your best friend.

Darcy–Weisbach equation: Δh = f (L/D) (V²/2g)

For steel pipes of various diameters,  The Engineering Toolbox has a handy chart. You can use this chart for other pipes, including copper and PVC.

When using these charts, you need to know the type of pipe, its inner diameter, and your rate of flow, which you should calculate with the previous equation.

Once you identify the diameter and flow rate, you can locate the corresponding pressure drop on the charts. We usually represent pressure drop in PSI.

How to Calculate the Valve Flow Coefficient

The equation for the valve flow coefficient is quite complicated. Let’s go through the equations step by step.

Step 1: Determine the Variables

The first step in any equation is to figure out the numbers you’ll plug into the variables. Remember, we need to find out the relevant answers for specific gravity (SG), rate of flow (Q), and our pressure drop (P).

For our example, we’ll use water, which has an SG of 1.00. The rate of flow will be 10.0 GPM. We’ll also be using a two-inch inner diameter PVC pipe, and knowing this will help us uncover our pressure drop. In the case of a two-inch PVC pipe, the P will be 0.11, according to this chart.

So for this example, our variables look like this:

• Pressure drop = ΔP = 0.11 PSI
• Specific gravity = SG = 1.00 (dimensionless)
• Rate of flow = Q = 10.00 GPM

Step 2: Plug the Values into the Equation

For those of you who skipped the earlier section, the equation for calculating the valve flow coefficient is  Cv = Q√(SG / ΔP). Now that we’ve ascertained the values for our variables, we can plug them into the equation. Once we do that, our example should look like this: Cv = 10 √ (1/0.11).

Step 3: Solve the Equation

Now that we’ve plugged our variables into the equation, we can work on solving it. Remember to always use your trusty high school PEMDAS when doing algebra so you can always come to the correct answer.

Since the equation has parentheses, we’ll start with those. Inside the parentheses is the SG divided by the P. So for our example, 1 divided by 0.11 gives us an answer of 9.0909 repeating. Next, we need to find the square root of that number. The square root of 9.0909 repeating is 3.0151134457776.

Now that we found the square too, the last calculation is easy. Multiply the Q by the number we just solved for. The calculation should be 10 multiplied by 3.0151134457776, giving us an answer of 30.151134457776.

So, through our example, we found that the valve flow coefficient (Cv) is rounded out to equal 30.15, which these 2” brass solenoid valves or 2” stainless steel solenoid valves can handle.

As you can probably tell, the calculation itself wasn’t too tricky. The most problematic aspect of figuring out the valve flow coefficient is ascertaining the correct values for the variables.

Two More Practice Problems

Let’s see if your calculation skills are up to snuff. In this section, I’ll give you two sets of variables. All you need to do is calculate the valve flow coefficient using the same equation as before.

Variable Set #1

• Rate of flow (Q) = 5.00 GPM
• Specific gravity (SG) = 0.8
• Pressure drop (ΔP) = 1.02 PSI

Answer: Cv ≈ 4.43

Variable Set #2

• Rate of flow (Q) = 2.00 GPM
• Specific gravity (SG) = 1.5
• Pressure drop (ΔP) = 0.57 PSI

Answer: Cv ≈ 3.24