1. What is Flow Rate from Pressure Difference?

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 laminar flow rates in pipes for various applications like plumbing, chemical processing, and biomedical systems.

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 describes laminar flow of incompressible Newtonian fluids in long, straight pipes with constant circular cross-sections.

3. Importance of Flow Rate Calculation

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

4. Using the Calculator

Tips: Enter the pipe radius (in meters), pressure difference (in Pascals), fluid viscosity (default is water at 20°C: 0.001002 Pa·s), and pipe length (in meters). 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 with constant circular cross-sections.

Q2: What's a typical viscosity value for water?
A: Water at 20°C has a dynamic viscosity of about 0.001002 Pa·s (the default value in the calculator).

Q3: How does pipe radius affect flow rate?
A: Flow rate is extremely sensitive to radius changes since it depends on r⁴ - doubling the radius increases flow rate by 16 times!

Q4: What are the limitations of this equation?
A: It assumes steady, laminar flow of incompressible Newtonian fluids in long pipes with no-slip boundary conditions.

Q5: How do I know if my flow is laminar?
A: Calculate the Reynolds number (Re = ρvD/μ). Flow is typically laminar when Re < 2100.