Flow Rate Calculator by Pressure and Diameter

Flow Rate Formula:

\[ Q = \frac{\pi \times (D/2)^4 \times \Delta P}{8 \times \mu \times L} \]

Diameter (D):

meters

Pressure Difference (ΔP):

Viscosity (μ):

Pa·s

Length (L):

meters

Flow Rate (Q):

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1. What is a Flow Rate Calculator by Pressure and Diameter?

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

Purpose: It helps engineers and scientists determine fluid flow characteristics in pipes and channels under laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ Q = \frac{\pi \times (D/2)^4 \times \Delta P}{8 \times \mu \times L} \]

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( D \) — Pipe diameter (meters)
\( \Delta P \) — Pressure difference (Pascals)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Pipe length (meters)

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 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 diameter, pressure difference, 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 flow regime does this equation apply to?
A: The Hagen-Poiseuille equation applies only to laminar (not turbulent) flow in circular pipes.

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

Q3: How does diameter affect flow rate?
A: Flow rate is proportional to the fourth power of the radius, so small diameter changes have large effects.

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

Q5: How do I calculate Reynolds number to check flow regime?
A: Use \( Re = \frac{\rho \times v \times D}{\mu} \), where ρ is density and v is velocity.