PSI to GPM Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Jul 04, 2022

Omni's PSI to GPM calculator allows you to determine water's flow rate in GPM from the PSI reading of a pressure gauge. You can also use this calculator to convert PSI to gallons per hour.

Continue reading this article to learn:

  • The difference between PSI and GPM.
  • What is Bernoulli's equation?
  • How to calculate GPM from PSI and pipe size?

PSI and GPM

PSI or pounds per square inch is a unit of pressure. We can define 1 psi as the pressure due to a force of one pound-force applied on an area of one square inch. Thus, a more accurate term for psi would be pound-force per square inch (lbf/in2).

One psi is approximately equal to 6894.76 pascals (the SI unit of pressure is pascal or Pa). It is very commonly used in measuring pressure in industries and everyday life, for example, tire pressure, fire hydrant pressure, etc.

GPM or gallons per minute is a unit of flow rate, i.e., it specifies how fast a liquid (for example, water) moves through a pipe or pump. One US gallon per minute is approximately equal to 6.309×105 m3/s6.309 × 10^{-5}\ \rm{m^3/s}.

Since PSI is a measure of pressure and GPM is a measure of flow rate, we can not directly convert one into another. However, we can use Bernoulli's equation for an incompressible fluid to calculate the flow rate in GPM if certain other variables are known.

Before going further, let us first try to understand what Bernoulli's equation is?

What is Bernoulli's equation?

Bernoulli's equation states that for an incompressible, frictionless fluid, the sum of pressure (PP), kinetic energy density, and potential energy density is constant, i.e.:

P+12ρv2+ρgh=constant\scriptsize P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}

where:

  • ρρ — Density of the fluid;
  • vv — Velocity of the fluid flow;
  • hh — Height from the ground; and
  • ggAcceleration due to gravity.

The potential energy density is calculated with the use of a modified potential energy equation, with density instead of mass of the fluid.

When the fluid flows through a pipe that has varying diameter and height, the pressure and energy densities at two locations along the pipe are related as:

P1+12ρv12+ρgh1=P2+12ρv22+ρgh2\scriptsize P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2
A typical geometry used for the derivation of Bernoulli's equation.
A typical geometry used for the derivation of Bernoulli's equation. (Source: wikimedia.org)

For a fluid flowing at a constant depth/height, the above equation changes to:

P1+12ρv12=P2+12ρv22\scriptsize P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2

In other words, as the speed of a moving fluid increases, its pressure drops and vice-versa. In the next section, we will see how to calculate GPM from pressure.

Calculating GPM from pressure

To determine the flow rate in gallons per minute or GPM, we need to know the pressure at two different locations (say 1 and 2) along the flow path (or pipe). Using Bernoulli's equation for fluid flow at constant depth, we can write:

P1+12ρv12=P2+12ρv22\scriptsize P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2

or

P1P2=12ρ(v22v12)(v22v12)=2(P1P2)ρ\scriptsize \begin{align*} P_1 - P_2 &= \frac{1}{2} \rho (v_2^2 - v_1^2) \\ \\ (v_2^2 - v_1^2) & = \frac{2(P_1 - P_2)}{\rho} \end{align*}

Hence, to determine the velocity, we should take the pressure difference between the two points, multiply it by 2, divide the result by the density of water and then take its square root.

Once we have the velocity, we can easily calculate the flow rate by multiplying it with the pipe's cross-sectional area. It is to be noted that here we are assuming that the cross-sectional area of the pipe is negligible as compared to the cross-sectional area of the tank. The velocity of water inside the tank is also taken to be negligible for all practical purposes, i.e., v1=0v_1 = 0.

How to calculate GPM from PSI and pipe size?

Let us see how we can calculate the flow rate of water as it exits from a tank through a pipe of diameter 2.5 inches. Let the pressure inside the tank be 72.0 psi. The pressure at the exit point will be equal to the atmospheric pressure, i.e., 14.7 psi.

  1. First we calculate the difference between the pressure inside the tank (P1P_1) and at the exit point (P2P_2):
P1P2=(72.014.7) psi=57.3 psi\quad \scriptsize \quad \begin{align*} P_1 - P_2 &= (72.0 - 14.7) \ \rm{psi} \\ &= 57.3 \ \rm{psi} \end{align*}
  1. To convert from pound-force per square inch (psi) to pound-force per square foot; we will multiply the result by 144:
57.3 psi×144 lbf/ft21 psi=8251.2 lbf/ft2\quad \scriptsize \quad \begin{align*} 57.3\ \rm{psi} \times \frac{144 \ \rm{lbf/ft^2}}{1\ \rm{psi}}\\ = 8251.2\ \rm{lbf/ft^2} \end{align*}
  1. We can also express lbf (pound-force) as 32.174 lb⋅ft/s². Therefore, we can rewrite the above pressure difference as:
8251.2×32.174 (lbft/s2)ft²=265,474.11 lb/fts2\quad \scriptsize \quad \begin{align*} 8251.2 \times 32.174\ \frac{(\rm{lb⋅ft/s^2)}}{\rm{ft²}} \\ = 265,474.11\ \rm{lb/ft⋅s^2} \end{align*}
  1. Now we multiply the difference in pressure by 2 and divide the result by the density of water (62.4 lb/ft3).
265,474.11 lb/fts2×262.4 lb/ft3=8,508.79 ft2/s2\quad \scriptsize \quad \begin{align*} & \frac{265,474.11\ \rm{lb/ft⋅s^2} \times 2} {62.4\ \rm{lb/ft^3}}\\ &=8,508.79\ \rm{ft^2/s^2} \end{align*}
  1. Taking the square root of the above value we will get the velocity in ft/s:
8,508.79 ft2/s2=92.243 ft/s\quad \scriptsize \quad \begin{align*} \sqrt{8,508.79\ \rm{ft^2/s^2}}=92.243 \ \rm{ft/s} \end{align*}
  1. Now we will calculate the cross-sectional area of the pipe:
Area=π(diameter2)2=3.14×(0.20833 ft2)2=0.03409 ft2\quad \scriptsize \quad \begin{align*} Area &= \pi \left (\frac{\text{diameter}}{2} \right )^2 \\ & = 3.14 \times\left (\frac{\text{0.20833\ \rm{ft}}}{2} \right )^2 \\ & = 0.03409 \ \rm{ft^2} \end{align*}
  1. Multiply the velocity by the cross-sectional area of the pipe:
92.243 ft/s×0.03409 ft2=3.145 ft3/s\quad \scriptsize \quad \begin{align*} & 92.243 \ \rm{ft/s} \times 0.03409 \ \rm{ft^2} \\ & = 3.145 \ \rm{ft^3/s} \end{align*}
  1. To convert cubic feet per second to gallons per minute, we multiply by 448.83:
3.145 ft3/s×448.83 gpm1 ft3/s=1411.57 gpm\quad \scriptsize \quad \begin{align*} & 3.145 \ \rm{ft^3/s} \times 448.83 \ \frac{\rm{gpm}}{1\ \rm{ft^3/s}}\\ & = 1411.57 \ \rm{gpm} \end{align*}

Whoa! That was not so easy 😰. Now let's see if using the psi to gallons per minute calculator can make our life easier.

How to use the PSI to GPM calculator?

We will consider the same problem as in the previous section:

  1. Type in the pressure inside the tank (72.0 psi) and the pressure at the exit (14.7 psi).

  2. Input the diameter of the pipe (2.5 inches). You can also enter the cross-sectional area of the pipe.

  3. The psi to gallons per minute calculator will display the flow rate in gallons per minute (1411.3 gpm).

  4. You can also use this calculator to convert psi to gallons per hour by choosing the unit from the drop-down menu.

FAQ

How do I calculate PSI from GPM and pipe diameter?

To calculate PSI from GPM and pipe diameter, proceed as follows:

  1. Calculate the cross-sectional area of the pipe using the given diameter.

  2. Divide the flow rate measured in GPM by the area and take the square of the result.

  3. Multiply the value from step 2 with the density of water and divide by 2.

  4. Add the atmospheric pressure to the result from step 3, and you will get the pressure in PSI.

How do I calculate GPM from PSI for water?

To calculate GPM from pressure in PSI for water, follow these steps:

  1. Measure the pressure inside the tank using a pressure gauge.

  2. Subtract the atmospheric pressure from the tank pressure.

  3. Multiply the result from step 2 by 2 and divide by the density of water.

  4. Take the square root of the value from step 3 and multiply it with the cross-sectional area of the pipe.

  5. Congrats! You have calculated the flow rate in gallons per minute (GPM) from the PSI reading of the pressure gauge.

Is GPM the same as PSI?

No, GPM (or gallons per minute) measures the flow rate of liquid, whereas PSI (or pounds per square inch) measures the pressure. Hence, they do not measure the same physical quantity.

How do I find flow rate from velocity?

Flow rate is the volume of fluid flowing per unit time through a given area. To determine flow rate from velocity, you should multiply the velocity by the cross-sectional area.

Purnima Singh, PhD
Pressure inside the tank
psi
Pressure at the exit
psi
Diameter of the pipe
in
Cross sectional area of the pipe
in²
Flow rate in gpm
US gal/min
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