PSI to GPM Calculator

Pressure inside the tank (PSI): PSI

Pressure at the exit (PSI): PSI

Diameter of the pipe:

Cross-sectional area unit:

Flow rate unit:

1. What is PSI to GPM Calculator?

Definition: This calculator converts pressure readings (in PSI) to flow rate in various units by using the pressure difference between two points and the pipe's diameter, applying Bernoulli's equation.

Purpose: It is used in fluid dynamics, plumbing, and engineering to determine the flow rate of water exiting a tank through a pipe, which is essential for designing and optimizing water systems.

2. How Does the Converter Work?

The converter uses the following steps based on Bernoulli's equation:

Formulas:

Pressure difference: \[ \Delta P = P_{\text{tank}} - P_{\text{exit}} \]
Velocity (using Bernoulli's equation): \[ v = \sqrt{\frac{2 \times \Delta P}{\rho}} \]
Cross-sectional area of the pipe: \[ A = \pi \times \left(\frac{\text{diameter}}{2}\right)^2 \]
Flow rate (cubic feet per second): \[ Q = v \times A \]
Flow rate in US GPM: \[ \text{US GPM} = Q \times 448.83 \]

Where:

\( \Delta P \): Pressure difference in PSI, converted to lb/ft² (\( 1 \, \text{PSI} = 144 \, \text{lb/ft}^2 \))
\( \rho \): Density of water (1.94 slugs/ft³)
\( v \): Velocity in ft/s
\( \text{diameter} \): Pipe diameter in feet (converted from selected unit)
\( A \): Cross-sectional area in ft² (converted to selected unit for display)
\( Q \): Flow rate in ft³/s
448.83: Conversion factor from ft³/s to US GPM

Unit Conversions:

Diameter:
- 1 mm = 0.00328084 ft
- 1 cm = 0.0328084 ft
- 1 m = 3.28084 ft
- 1 inch = 0.0833333 ft
- 1 ft = 1 ft
Cross-sectional Area:
- 1 ft² = 92903.04 mm²
- 1 ft² = 929.0304 cm²
- 1 ft² = 0.09290304 m²
- 1 ft² = 144 in²
- 1 ft² = 1 ft²
Flow Rate:
- 1 US gal/min = 1/60 US gal/s
- 1 US gal/min = 60 US gal/hr
- 1 US gal/min = 1440 US gal/day
- 1 US gal/min = 0.832674 UK gal/min
- 1 US gal/min = 0.832674 / 60 UK gal/s
- 1 US gal/min = 0.832674 × 60 UK gal/hr
- 1 US gal/min = 0.832674 × 1440 UK gal/day

Steps:

Enter the pressure inside the tank, pressure at the exit, and the diameter of the pipe with its unit.
Select the units for cross-sectional area and flow rate.
Validate the inputs to ensure they are positive and that tank pressure is greater than exit pressure.
Convert the diameter to feet and calculate the pressure difference.
Compute the velocity using Bernoulli's equation.
Calculate the cross-sectional area in ft², then convert to the selected unit.
Compute the flow rate in US gal/min, then convert to the selected unit.
Display the results, using scientific notation for values less than 0.001, otherwise with 4 decimal places.

3. Importance of PSI to GPM Conversion

Converting PSI to GPM is crucial for:

Plumbing Design: Ensures proper sizing of pipes and pumps for water systems.
Irrigation Systems: Determines the flow rate needed for efficient water delivery.
Industrial Applications: Helps in managing fluid flow in manufacturing processes.

4. Using the Converter

Example: Convert a tank pressure of 72.0 PSI, exit pressure of 14.7 PSI, and pipe diameter of 63.5 mm to GPM, with area in cm² and flow rate in US gal/hr.

Enter the values: tank pressure = 72.0 PSI, exit pressure = 14.7 PSI, diameter = 63.5 mm, area unit = cm², flow unit = US gal/hr.
The converter calculates:
- Convert diameter to feet: \( 63.5 \times 0.00328084 = 0.208333 \, \text{ft} \)
- Pressure difference: \( \Delta P = 72.0 - 14.7 = 57.3 \, \text{PSI} \)
- Convert to lb/ft²: \( 57.3 \times 144 = 8251.2 \, \text{lb/ft}^2 \)
- Velocity: \( v = \sqrt{\frac{2 \times 8251.2}{1.94}} \approx 92.232 \, \text{ft/s} \)
- Cross-sectional area: \( A = \pi \times \left(\frac{0.208333}{2}\right)^2 \approx 0.034087 \, \text{ft}^2 \)
- Area in cm²: \( 0.034087 \times 929.0304 \approx 31.6632 \, \text{cm}^2 \)
- Flow rate (ft³/s): \( Q = 92.232 \times 0.034087 \approx 3.1445 \, \text{ft}^3/\text{s} \)
- Flow rate (US GPM): \( \text{US GPM} = 3.1445 \times 448.83 \approx 1411.2855 \, \text{US gal/min} \)
- Flow rate (US gal/hr): \( 1411.2855 \times 60 \approx 84677.1300 \, \text{US gal/hr} \)
The converter returns:
- Cross-sectional area: 31.6632 cm²
- Flow rate: 84677.1300 US gal/hr

5. Frequently Asked Questions (FAQ)

Q: What is the PSI to GPM Calculator?
A: The PSI to GPM Calculator converts pressure readings (in PSI) to flow rate in various units using Bernoulli's equation, given the pressure difference and pipe diameter.

Q: Why is Bernoulli's equation used?
A: Bernoulli's equation relates pressure and velocity in a fluid, allowing us to calculate the flow rate based on pressure differences.

Q: How is the PSI to GPM Calculator used in real life?
A: It is used in plumbing, irrigation, and industrial applications to determine the flow rate of water through pipes, aiding in system design and optimization.