1. What is the Flow Rate Calculator from Pressure Difference?

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

Purpose: It helps engineers and scientists determine fluid flow rates in laminar flow conditions based on pressure differences.

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

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are essential for designing fluid systems, predicting performance, and ensuring proper operation of pipelines and channels.

4. Using the Calculator

Tips: Enter the 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 are the limitations of this equation?
A: The Hagen-Poiseuille equation applies only to laminar flow (Re < 2100) in long, straight, circular pipes with Newtonian fluids.

Q2: What's a typical viscosity value for water?
A: Water at 20°C has a viscosity of about 0.001 Pa·s. Viscosity decreases with increasing temperature.

Q3: How does pipe radius affect flow rate?
A: Flow rate is proportional to the fourth power of radius - doubling the radius increases flow rate by 16 times.

Q4: What units should I use?
A: Use consistent SI units: meters for dimensions, Pascals for pressure, and Pa·s for viscosity.

Q5: Can I use this for turbulent flow?
A: No, for turbulent flow you would need to use the Darcy-Weisbach equation instead.