1. What is a Flow Rate Calculator by Pressure and Diameter?

Definition: This calculator estimates the volumetric flow rate in a pipe using the Hagen-Poiseuille equation for laminar flow conditions.

Purpose: It helps engineers and fluid dynamics professionals determine flow rates in pipes based on pressure difference and pipe dimensions.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

Where:

• \( Q \) — Volumetric flow rate (m³/s)
• \( r \) — Pipe radius (m)
• \( \Delta P \) — Pressure difference (Pa)
• \( \mu \) — Dynamic viscosity (Pa·s)
• \( L \) — Pipe length (m)

Explanation: The equation relates flow rate to the fourth power of the pipe radius, showing that small changes in diameter significantly affect flow.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are essential for designing piping systems, predicting fluid behavior, and ensuring proper system operation.

4. Using the Calculator

Tips: Enter pipe radius (half of diameter), pressure difference, fluid viscosity (default 0.001 Pa·s for water at 20°C), and pipe length (default 1m). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What flow regimes does this equation apply to?
A: The Hagen-Poiseuille equation is valid only for laminar flow (typically Re < 2100).

Q2: How does pipe roughness affect the calculation?
A: This equation assumes smooth pipes. For rough pipes or turbulent flow, use the Darcy-Weisbach equation instead.

Q3: What's a typical viscosity value for water?
A: Water at 20°C has viscosity of about 0.001 Pa·s. Viscosity decreases with temperature.

Q4: Why is radius to the fourth power important?
A: This strong dependence means doubling pipe diameter increases flow rate by 16 times (2⁴) for the same pressure.

Q5: How do I convert from diameter to radius?
A: Simply divide the diameter by 2. The calculator requires radius as input.