Calculate GPM From PSI And Pipe Size

Poiseuille's Law Formula:

\[ Q = \frac{\pi \times r^4 \times \Delta P}{8 \times \mu \times L} \times \frac{3.785 \times 60}{1000} \]

Pipe Radius (r):

meters

Pressure Difference (ΔP):

Pascals

Viscosity (μ):

Pa·s

Pipe Length (L):

meters

Flow Rate (Q):

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1. What is Poiseuille's Law?

Poiseuille's Law describes the flow of fluid through a cylindrical pipe. It relates the volumetric flow rate to the pressure difference, pipe dimensions, and fluid viscosity. This calculator converts the result to gallons per minute (GPM) for practical applications.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law formula:

\[ Q = \frac{\pi \times r^4 \times \Delta P}{8 \times \mu \times L} \times \frac{3.785 \times 60}{1000} \]

Where:

\( Q \) — Flow rate in gallons per minute (GPM)
\( r \) — Pipe radius in meters
\( \Delta P \) — Pressure difference in Pascals
\( \mu \) — Dynamic viscosity in Pascal-seconds (Pa·s)
\( L \) — Pipe length in meters
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula calculates flow in cubic meters per second, then converts to GPM using the conversion factors 3.785 (liters/gallon), 60 (seconds/minute), and 1000 (liters/cubic meter).

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, selecting pumps, optimizing fluid transport, and ensuring efficient operation in industrial, plumbing, and engineering applications.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure radius, pressure difference, viscosity, and length are positive values. For water at 20°C, viscosity is approximately 0.001 Pa·s.

5. Frequently Asked Questions (FAQ)

Q1: What are typical viscosity values for common fluids?
A: Water (20°C): 0.001 Pa·s, Air (20°C): 0.000018 Pa·s, Engine Oil: 0.1-0.3 Pa·s, Honey: 2-10 Pa·s.

Q2: How do I convert PSI to Pascals?
A: 1 PSI = 6894.76 Pascals. Multiply PSI value by 6894.76 to get Pascals.

Q3: What are the limitations of Poiseuille's Law?
A: Assumes laminar flow, Newtonian fluid, steady flow, and no-slip boundary conditions. Not accurate for turbulent flow or non-Newtonian fluids.

Q4: How does pipe roughness affect the calculation?
A: Poiseuille's Law assumes smooth pipes. For rough pipes, additional friction factors must be considered, especially in turbulent flow regimes.

Q5: Can this be used for gas flow calculations?
A: Yes, but only for laminar flow conditions. For gases, compressibility effects may need to be considered at higher pressure differences.