Flow Rate Equation Pressure

Flow Rate Formulas:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ Q = V \times A \times 448.83 \]

P₁ (Upstream Pressure):

psi

P₂ (Downstream Pressure):

psi

ρ (Fluid Density):

lb/ft³

A (Cross-sectional Area):

ft²

V (Velocity): ft/s

Q (Flow Rate): GPM

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1. What is the Flow Rate Equation from Pressure?

Definition: This calculator determines the flow rate (GPM) through a pipe or channel using Bernoulli's equation based on pressure difference, fluid density, and cross-sectional area.

Purpose: It helps engineers and technicians calculate fluid flow rates in piping systems, hydraulic systems, and process equipment.

2. How Does the Calculator Work?

The calculator uses two formulas:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ Q = V \times A \times 448.83 \]

Where:

\( V \) — Fluid velocity (ft/s)
\( P_1 \) — Upstream pressure (psi)
\( P_2 \) — Downstream pressure (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Flow rate (gallons per minute, GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: The pressure difference is converted to velocity, which is then used to calculate volumetric flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are essential for system design, pump sizing, process control, and ensuring proper operation of fluid systems.

4. Using the Calculator

Tips: Enter both pressures in psi, fluid density in lb/ft³ (water is 62.4 lb/ft³), and cross-sectional area in ft². All values must be > 0 except P₂ which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What units does this calculator use?
A: The calculator uses imperial units: psi for pressure, lb/ft³ for density, ft² for area, ft/s for velocity, and GPM for flow rate.

Q2: What's the 144 factor in the equation?
A: This converts psi (lb/in²) to lb/ft² (1 ft² = 144 in²).

Q3: What's the 448.83 conversion factor?
A: This converts ft³/s to gallons per minute (1 ft³/s = 448.83 GPM).

Q4: Does this account for friction losses?
A: No, this is the theoretical maximum flow. For real systems, you'll need to account for pipe friction and other losses.

Q5: What if P₂ is greater than P₁?
A: The calculator will show an error as flow would be in the opposite direction.