Flow Rate Calculator Pressure and Diameter

Hagen-Poiseuille Equation:

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

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 diameter, pressure difference, fluid viscosity, and pipe length.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

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, making diameter the most significant factor in determining flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, understanding fluid dynamics, and optimizing industrial processes involving fluid transport.

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, incompressible Newtonian fluid, no-slip condition at pipe walls, and steady-state conditions.

Q2: When is this equation not applicable?
A: For turbulent flow (Reynolds number > ~2000), non-Newtonian fluids, or very short pipes where entrance effects are significant.

Q3: How does pipe roughness affect the flow rate?
A: The equation assumes smooth pipes. Roughness becomes important in turbulent flow but has negligible effect in laminar flow.

Q4: Why is diameter to the fourth power so important?
A: This strong dependence means small increases in diameter dramatically increase flow capacity, while small decreases significantly reduce it.

Q5: What's the relationship to Reynolds number?
A: The equation is valid when Re < 2000 (laminar flow). For higher Re, the Darcy-Weisbach equation should be used instead.