Flow Rate Calculator Using Pressure

Flow Rate Formula:

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

Radius (r):

Pressure Difference (ΔP):

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

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1. What is a Flow Rate Calculator Using Pressure?

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 pipes under pressure gradients, particularly for laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

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

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 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 the pipe radius (in meters), pressure difference (in Pascals), fluid viscosity (default 0.001 Pa·s 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 long, straight, circular pipes.

Q2: Why does radius have such a large effect (r⁴)?
A: The radius affects both the cross-sectional area (r²) and the velocity profile (another r²), resulting in the r⁴ dependence.

Q3: What's a typical viscosity value for water?
A: Water at 20°C has a viscosity of about 0.001 Pa·s, which is the default value in the calculator.

Q4: Can I use this for gases?
A: Only for gases in laminar flow conditions. Gas viscosity is much lower than liquids (typically 0.00001 to 0.00002 Pa·s for air).

Q5: How do I convert the result to other units?
A: 1 m³/s = 1000 L/s = 15850 gpm (gallons per minute). For smaller flows, results might be in mL/s (1 m³/s = 1,000,000 mL/s).