1. What is Flow Rate from Pressure Calculation?

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

Purpose: It helps engineers and scientists calculate fluid flow in pipes when pressure difference is known, particularly for laminar flow conditions.

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: Flow rate is directly proportional to the pressure difference and the fourth power of the radius, and inversely proportional to viscosity and pipe length.

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 in chemical, mechanical, and civil engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this equation apply to?
A: The Hagen-Poiseuille equation applies only to laminar (not turbulent) flow in circular pipes.

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

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

Q4: How do I convert between different pressure units?
A: 1 Pa = 0.000145 psi, 1 bar = 100,000 Pa. Use our unit converter if needed.

Q5: What if my flow is turbulent?
A: For turbulent flow, you would need to use the Darcy-Weisbach equation instead.