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Flow Rate Calculator with Pressure

Flow Rate Formula:

\[ Q = \frac{\pi \times r^4 \times \Delta P}{8 \times \mu \times L} \]

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Pa
Pa·s
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1. What is a Flow Rate Calculator with Pressure?

Definition: This calculator computes 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 pipes under pressure differences, useful in hydraulic systems, medical applications, and industrial processes.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ Q = \frac{\pi \times r^4 \times \Delta P}{8 \times \mu \times L} \]

Where:

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 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 0.001 Pa·s for water at 20°C), and pipe length (default 1 meter). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What fluids does this equation apply to?
A: The Hagen-Poiseuille equation applies to Newtonian fluids in laminar flow through cylindrical pipes.

Q2: Why does radius have such a large effect (r⁴)?
A: The r⁴ relationship means small changes in pipe diameter dramatically affect flow rate due to reduced friction near the pipe walls.

Q3: 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 temperature.

Q4: What are the limitations of this equation?
A: It assumes steady, laminar flow of incompressible Newtonian fluids in straight, rigid pipes with no slip at walls.

Q5: How do I convert the result to other units?
A: 1 m³/s = 1000 L/s = 15850 gpm (gallons per minute). For different units, use appropriate conversion factors.

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