Flow Calculator with 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 Calculator with 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 laminar flow conditions based on pressure differences and pipe characteristics.

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:

\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Pipe radius (m)
\( \Delta P \) — Pressure difference (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Length of pipe (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 various engineering applications.

4. Using the Calculator

Tips: Enter the pipe radius in meters, pressure difference in Pascals, fluid viscosity in Pa·s (default 0.001 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 circular pipes.

Q2: Why does radius have such a large effect (r⁴)?
A: The r⁴ dependence comes from the velocity profile integration and shows how dramatically pipe diameter affects flow rate.

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: The equation can be used for gases in laminar flow, but note that gases are compressible and viscosity changes with temperature.

Q5: What are the limitations of this equation?
A: It assumes steady, laminar flow of Newtonian fluids in straight, circular pipes with no-slip boundary conditions.