Pressure differences develop all the time across fluid devices: learn how to calculate the differential pressure, the conversion to flow rate and flow factor, and much more with our tool!

Keep reading this short article to learn:

  • What is differential pressure?
  • What is the flow coefficient, and how to calculate it;
  • How to use the flow rate to calculate the pressure difference; and
  • Examples of applications of the two formulas.

What is the differential pressure? What is the relationship between pressure and flow rate?

The differential pressure measures the reduction/increase of pressure in a fluid between two sections of conduct as a function of the flow and other parameters.

The pressure difference may depend on various factors. Just to cite some of them, remember the geometric ones, as for constriction or widening of the conduct, or the kinematic ones, such as increases in the roughness of the inner surface of the piping, or, again, environmental ones.

In many devices operating with fluids, the differential pressure is a fundamental quantity to analyze their operations and proper functioning. One of the quantities related to the differential pressure is the rate of flow in the conduct. Together, the rate of flow and differential pressure define the flow factor or flow coefficient.

🙋 The only difference between flow factor and flow coefficient is your choice of measurement units: the flow coefficient is expressed in imperial units, while the flow factor uses metric units.

What is the flow coefficient? How do I use the differential pressure to calculate the flow coefficient?

The flow coefficient measures how well a device operating with a fluid reacts to a differential pressure for varying flow values. We measure the flow coefficient with the formula:

CVKV=QSΔPC_\text{V} \equiv K_\text{V} = Q\cdot\sqrt\frac{S}{\Delta P}

In the flow coefficient/flow factor formula from differential pressure and flow rate, pay attention to the following things.

  • We equate the flow coefficient CVC_\text{V} with the flow factor KVK_{\text{V}} since they only differ in measurement units.
  • We find:
    • The flow rate QQ;
    • The specific gravity SS; and
    • The differential pressure ΔP\Delta P.

🔎 Learn how to calculate these quantities with our purposefully built tools: the flow rate calculator. the pressure calculator, and the specific gravity calculator.

The measurement units for these quantities are:

  • Volume per time unit for the flow rate. In the metric system, we use m3/s\text{m}^3/\text{s}, while in the imperial system, we can use US gals/min\text{US gals}/\text{min}.
  • Pressure for the differential pressure. Use either bar\text{bar} or PSI\text{PSI}.
  • No units for the specific gravity. This quantity is a measurement of a fluid's density compared to water at room temperature.

🔎 If you need help converting the pressure in your desired units, use our pressure converter!

How do I calculate the differential pressure from flow rate and flow coefficient?

If you know the flow characteristic of your device, you can calculate the differential pressure from one end to the other. This conversion from pressure to flow is associated with the following differential pressure formula:

ΔP=S(QKV)2=S(QCV)2\Delta P = S\cdot\left(\frac{Q}{K_\text{V}}\right)^2=S\cdot\left(\frac{Q}{C_\text{V}}\right)^2

The quantities you find in this differential pressure equation are the same we saw before.

When do we use the differential pressure?

Whenever you introduce a component or device into your fluid system, a pressure differential develops from one end to the other. As you know from the formula for the differential pressure, the flow changes accordingly. You can calculate the flow coefficient from the pressure differential: imagine having a valve with a flow rate of 1 US gal/s1\ \text{US gal}/\text{s}. The valve generates a differential pressure of 4 PSI4\ \text{PSI}. We are operating with water at 60 °F60\ \degree\text{F}: calculate the flow coefficient from the pressure.

CV=1 US gals14 PSI=14 US gals per PSI\begin{align*} C_{\text{V}} &= 1\ \frac{\text{US gal}}{\text{s}} \cdot \sqrt{\frac{1}{4\ \text{PSI}}} \\ &= \frac{1}{4}\ \frac{\text{US gal}}{\text{s}}\ \footnotesize\text{per PSI} \end{align*}

If you know the behavior of your device against a pressure difference, you can easily calculate the differential pressure that would develop under certain conditions. This allows you to properly design your fluid system. Use our tool to calculate from flow rate to pressure differential in a valve with flow coefficient 18 US gal/min18\ \text{US gal}/\text{min} per 1 PSI1\ \text{PSI}. Imagine to operate with a flow of 50 US gal/min50\ \text{US gal}/\text{min}, and use water once again:

ΔP=S(QCV)2=1(5018)2=112 PSI\begin{align*} \Delta P &=S\cdot\left(\frac{Q}{C_\text{V}}\right)^2 \\ &= 1\cdot\left(\frac{50}{18}\right)^2 = 112\ \text{PSI} \end{align*}
Davide Borchia
Fluid properties
Specific gravity
Flow properties
Discharge or volumetric flow rate
Flow factor
Differential pressure
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