How To Calculate Flow Rate From Pressure

Poiseuille's Equation:

\[ Q = \sqrt{ \frac{P \times \pi \times D^4}{128 \times \mu \times L} } \]

Pressure Drop (P):

Diameter (D):

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

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1. What Is Poiseuille's Equation?

Poiseuille's equation describes the flow rate of a fluid through a cylindrical pipe under laminar flow conditions. It relates flow rate to pressure drop, pipe dimensions, and fluid properties, providing fundamental insights into fluid dynamics in confined spaces.

2. How Does The Calculator Work?

The calculator uses Poiseuille's equation:

\[ Q = \sqrt{ \frac{P \times \pi \times D^4}{128 \times \mu \times L} } \]

Where:

\( Q \) — Flow rate (m³/s)
\( P \) — Pressure drop (Pa)
\( D \) — Pipe diameter (m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Pipe length (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The equation demonstrates that flow rate is proportional to the fourth power of diameter and directly proportional to pressure drop, while inversely proportional to viscosity and length.

3. Importance Of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, optimizing fluid transport, predicting pressure losses, and ensuring efficient operation in various engineering applications.

4. Using The Calculator

Tips: Enter pressure drop in Pascals, diameter in meters, viscosity in Pascal-seconds, and length in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What Are The Limitations Of Poiseuille's Equation?
A: The equation assumes laminar flow, Newtonian fluids, steady-state conditions, and no-slip boundary conditions. It may not accurately predict flow in turbulent conditions or with non-Newtonian fluids.

Q2: What Is Considered Laminar Flow?
A: Laminar flow typically occurs at Reynolds numbers below 2000, where fluid particles move in parallel layers with minimal mixing between layers.

Q3: How Does Diameter Affect Flow Rate?
A: Flow rate increases with the fourth power of diameter, meaning doubling the diameter increases flow rate by 16 times under the same pressure conditions.

Q4: When Should I Use This Equation?
A: Use for calculating flow in straight, circular pipes with constant cross-section under laminar flow conditions, commonly in medical devices, microfluidics, and small-scale fluid systems.

Q5: What Units Should I Use For Viscosity?
A: Use Pascal-seconds (Pa·s) in SI units. Common conversions: 1 cP = 0.001 Pa·s, 1 P = 0.1 Pa·s.