Find Flow Rate from Pressure and Diameter

Flow Rate Formulas:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ Q = V \times \pi \times \left(\frac{D}{2}\right)^2 \times 448.83 \]

Upstream Pressure (P₁):

psi

Downstream Pressure (P₂):

psi

Fluid Density (ρ):

lb/ft³

Pipe Diameter (D):

Velocity (V): ft/s

Flow Rate (Q): GPM

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1. What is Flow Rate from Pressure and Diameter?

Definition: This calculator determines the fluid velocity and volumetric flow rate through a pipe based on pressure difference and pipe diameter.

Purpose: It helps engineers and technicians in fluid systems design and analysis to estimate flow rates in piping systems.

2. How Does the Calculator Work?

The calculator uses two formulas:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ Q = V \times \pi \times \left(\frac{D}{2}\right)^2 \times 448.83 \]

Where:

\( V \) — Fluid velocity (ft/s)
\( P_1 \) — Upstream pressure (psi)
\( P_2 \) — Downstream pressure (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Volumetric flow rate (GPM)
\( D \) — Pipe diameter (ft)

Explanation: The first equation calculates velocity from pressure difference using Bernoulli's principle. The second converts velocity to flow rate using pipe cross-sectional area.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate estimation is crucial for system design, pump sizing, and ensuring proper operation of fluid systems.

4. Using the Calculator

Tips: Enter the pressure difference (P₁ - P₂), fluid density (default 62.4 lb/ft³ for water), and pipe diameter in feet. All values must be positive and P₁ > P₂.

5. Frequently Asked Questions (FAQ)

Q1: Why is the 144 factor included?
A: It converts psi to lb/ft² (1 psi = 144 lb/ft²) for consistent units in the calculation.

Q2: What's the 448.83 conversion factor for?
A: It converts ft³/s to gallons per minute (GPM) (1 ft³/s = 448.83 GPM).

Q3: What density should I use for other fluids?
A: Use 49.2 lb/ft³ for gasoline, 78.6 lb/ft³ for seawater, or look up your specific fluid's density.

Q4: Does this account for friction losses?
A: No, this is an ideal flow calculation. For real systems, consider additional factors like pipe roughness and length.

Q5: Can I use inches for pipe diameter?
A: Convert inches to feet first (divide by 12) as the formula requires feet.