Flow Rate Formula with Pressure

Flow Rate Formulas:

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

Inlet Pressure (P₁):

psi

Outlet Pressure (P₂):

psi

Fluid Density (ρ):

lb/ft³

Cross-Sectional Area (A):

ft²

Velocity (V): ft/s

Flow Rate (Q): GPM

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1. What is the Flow Rate Formula with Pressure?

Definition: This calculator determines fluid velocity and volumetric flow rate based on pressure difference, fluid density, and pipe cross-sectional area.

Purpose: It helps engineers and technicians calculate flow parameters in hydraulic systems and piping networks.

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)
\( P_1 \) — Inlet pressure (psi)
\( P_2 \) — Outlet pressure (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Volumetric flow rate (GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: The first equation calculates velocity from pressure difference using Bernoulli's principle, while the second converts this to flow rate in gallons per minute.

3. Importance of Flow Rate Calculation

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

4. Using the Calculator

Tips: Enter pressure values in psi, fluid density in lb/ft³ (default 62.4 for water), and cross-sectional area in ft². All values must be positive with density and area > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the 144 factor in the equation?
A: This converts psi (lb/in²) to lb/ft² (1 ft² = 144 in²).

Q2: Why 448.83 in the flow rate formula?
A: This converts ft³/s to gallons per minute (1 ft³/s = 448.83 GPM).

Q3: What's a typical fluid density value?
A: Water at 60°F is 62.4 lb/ft³. Other fluids have different densities (oil ~55, gasoline ~42 lb/ft³).

Q4: How do I find cross-sectional area?
A: For circular pipes: \( A = \pi \times (diameter/2)^2 \). Convert diameter to feet.

Q5: Does this account for friction losses?
A: No, this is ideal flow. For real systems, consider additional pressure drop calculations.