1. What is the Hydraulic Calculator for Pipe Flow?

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 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 radius, and inversely proportional to viscosity and pipe length.

3. Importance of Pipe Flow 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 difference, fluid viscosity (default 0.001002 Pa·s for water at 20°C), and pipe length. All values must be > 0.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is radius to the fourth power?
A: Flow rate is extremely sensitive to pipe diameter because of the parabolic velocity profile in laminar flow.

Q3: What's a typical viscosity value for water?
A: Water at 20°C has a viscosity of about 0.001002 Pa·s (the default value).

Q4: What are the limitations of this equation?
A: It assumes steady, incompressible, laminar flow of a Newtonian fluid in a pipe of constant circular cross-section.

Q5: How does temperature affect the calculation?
A: Temperature primarily affects viscosity. Warmer fluids typically have lower viscosity, resulting in higher flow rates.