Flow Through Pipe Calculator Pressure

Hagen-Poiseuille Equation:

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

Diameter (D):

Pressure Difference (ΔP):

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

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1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the volumetric flow rate of a fluid through a cylindrical pipe under laminar flow conditions. It relates the flow rate to the pipe dimensions, fluid properties, and pressure difference.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

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

Explanation: The equation shows that flow rate is proportional to the fourth power of the pipe diameter and the pressure difference, and inversely proportional to the viscosity and pipe length.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, predicting fluid behavior, and ensuring proper system operation in engineering applications.

4. Using the Calculator

Tips: Enter all values in SI units (meters for length/diameter, Pascals for pressure, Pa·s for viscosity). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Hagen-Poiseuille equation?
A: The equation assumes laminar flow, Newtonian fluid, steady state, no-slip condition at pipe walls, and constant fluid properties.

Q2: When is this equation not applicable?
A: It doesn't apply to turbulent flow, non-Newtonian fluids, very short pipes, or cases with significant entrance/exit effects.

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

Q4: What's the difference between Hagen-Poiseuille and Bernoulli equations?
A: Bernoulli considers energy conservation for ideal fluids, while Hagen-Poiseuille accounts for viscous effects in laminar flow.

Q5: Can this be used for gases?
A: Only for very slow gas flows where compressibility effects are negligible. For most gas flows, other equations are needed.