How to Convert Differential Pressure to Flow

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The field of fluid mechanics is concerned with studying the movement of fluids. One of the cornerstones of this field is Bernoulli's equation, named for the eighteenth-century scientist, Daniel Bernoulli. This equation relates many physical quantities in fluid mechanics into an elegant and simple-to-understand equation. For example, using Bernoulli's equation, it is possible to relate the differential pressure of a fluid (i.e., the difference in pressure of the fluid between two different points) with the flow of the fluid, which is important if you would like to measure how much fluid flows over a given amount of time.

    To find the velocity of the fluid flow, multiply the differential pressure by two and divide this number by the density of the flowing material. As an example, assuming a differential pressure of 25 Pascals (or Pa, the unit of measurement of pressure) and the material is water, which has a density of 1 kilogram per meter cubed (kg/m^3), the resulting number will be 50 meters squared per seconds squared (m^2/s^2). Call this result A.

    Find the square root of result A. Using our example, the square root of 50 m^2/s^2 is 7.07 m/s. This is the velocity of the fluid.

    Determine the area of the pipe the fluid is moving through. For example, if the pipe has a radius of 0.5 meters (m), the area is found by squaring the radius (i.e. multiplying the area by itself) and multiplying by the constant pi (keeping as many decimal places as possible; the value of pi stored in your calculator will suffice). In our example, this gives 0.7854 meters squared (m^2).

    Calculate the flow rate by multiplying the fluid velocity by the area of the pipe. Concluding our example, multiplying 7.07 m/s by 0.7854 m^2 gives 5.55 meters cubed per second (m^3/s). This is the fluid flow rate.


    • During your calculation, carry as many decimal places as you can throughout the intermediate steps, then round the number down in the last step.

      When multiplying by the constant pi, try to keep as many decimal places as you can, as rounding may lead to small errors.


    • These steps assume fluid flow in a horizontal pipe. If there is a vertical component to the fluid flow, these steps will not apply.

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