1. What is a Pipe Flow Rate Calculator?

Definition: This calculator determines the volumetric flow rate of a fluid through a cylindrical pipe using the Hagen-Poiseuille equation.

Purpose: It helps engineers and fluid dynamics professionals analyze laminar flow conditions in pipes.

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 drop along the pipe (Pa)
• \( \eta \) — Dynamic viscosity of the fluid (Pa·s)
• \( L \) — Length of the pipe (m)

Explanation: The equation describes laminar flow of an incompressible, Newtonian fluid in a long cylindrical pipe.

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 the pipe radius, pressure drop, fluid viscosity (default 0.001 Pa·s for water at 20°C), and pipe length. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What types of flow does this equation apply to?
A: The Hagen-Poiseuille equation applies only to laminar (not turbulent) flow in long, straight pipes.

Q2: Why is radius to the fourth power so important?
A: The r⁴ term means small changes in pipe radius dramatically affect flow rate - double the radius increases flow 16 times!

Q3: What's a typical viscosity value for water?
A: Water at 20°C has η ≈ 0.001 Pa·s. Higher temperatures decrease viscosity.

Q4: How do I calculate pressure drop?
A: ΔP is the difference between inlet and outlet pressures. For horizontal pipes, it equals the pressure needed to overcome viscous friction.

Q5: What are the limitations of this equation?
A: It assumes steady, laminar flow of Newtonian fluids in straight pipes with no-slip boundary conditions.