Pipe Flow Capacity Calculator

Poiseuille's Equation:

\[ Q = \frac{\pi ID^4 \Delta P}{128 \mu L} \]

Internal Diameter (ID):

Pressure Difference (ΔP):

Viscosity (μ):

Pa·s

Length (L):

Flow Capacity (Q):

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1. What is Poiseuille's Equation?

Poiseuille's equation describes the flow capacity of a fluid through a cylindrical pipe. It relates the volumetric flow rate to the pipe dimensions, pressure difference, and fluid viscosity, assuming laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses Poiseuille's equation:

\[ Q = \frac{\pi ID^4 \Delta P}{128 \mu L} \]

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( ID \) — Internal diameter of the pipe (m)
\( \Delta P \) — Pressure difference along the pipe (Pa)
\( \mu \) — Dynamic viscosity of the fluid (Pa·s)
\( L \) — Length of the pipe (m)

Explanation: The equation shows that flow rate is proportional to the fourth power of the pipe diameter, making diameter the most influential factor in flow capacity.

3. Importance of Flow Capacity Calculation

Details: Accurate flow capacity calculation is essential for designing piping systems, selecting appropriate pump sizes, and ensuring efficient fluid transport in various engineering applications.

4. Using the Calculator

Tips: Enter all values in SI units. Internal diameter, pressure difference, viscosity, and length must be positive values. The calculator assumes laminar flow conditions (Re < 2300).

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Poiseuille's equation?
A: It assumes laminar flow, Newtonian fluid, constant viscosity, and no-slip conditions at the pipe wall. It's not accurate for turbulent flow or non-Newtonian fluids.

Q2: How does temperature affect the calculation?
A: Temperature affects fluid viscosity significantly. For accurate results, use viscosity values at the operating temperature.

Q3: Can this equation be used for gases?
A: Yes, but only for incompressible flow conditions where density changes are negligible (typically for Mach numbers < 0.3).

Q4: What is the Reynolds number range for laminar flow?
A: Typically, flow is laminar for Reynolds numbers below 2300, transitional between 2300-4000, and turbulent above 4000.

Q5: How does pipe roughness affect the calculation?
A: Poiseuille's equation assumes smooth pipes. For rough pipes, the actual flow rate may be lower due to increased friction.