Pipe Capacity Calculator Flowing Full

Hagen-Poiseuille Equation:

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

Inner Diameter (ID):

Pressure Drop (ΔP):

Viscosity (μ):

Pa·s

Length (L):

Flow Capacity:

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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 provides a mathematical relationship between flow rate, pipe dimensions, fluid properties, and pressure gradient.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

\( ID \) — Inner diameter of the pipe (m)
\( \Delta P \) — Pressure drop along the pipe (Pa)
\( \mu \) — Dynamic viscosity of the fluid (Pa·s)
\( L \) — Length of the pipe (m)
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: The equation assumes laminar flow, Newtonian fluid, and no-slip boundary conditions at the pipe wall.

3. Importance of Flow Capacity Calculation

Details: Accurate flow capacity calculation is crucial for pipe system design, fluid transport optimization, pump selection, and ensuring efficient operation of hydraulic systems in various engineering applications.

4. Using the Calculator

Tips: Enter all values in SI units (meters for length dimensions, Pascals for pressure, Pa·s for viscosity). All input values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of the Hagen-Poiseuille equation?
A: The equation is valid only for laminar flow (Re < 2300), Newtonian fluids, steady-state conditions, and fully developed flow in straight circular pipes.

Q2: How does pipe diameter affect flow capacity?
A: Flow capacity is proportional to the fourth power of the diameter, meaning small increases in diameter result in significant increases in flow capacity.

Q3: What is the typical viscosity range for common fluids?
A: Water at 20°C: ~0.001 Pa·s, Air: ~0.000018 Pa·s, Engine oil: ~0.1-0.3 Pa·s, Honey: ~2-10 Pa·s.

Q4: How does temperature affect the calculation?
A: Temperature affects viscosity significantly. For accurate results, use viscosity values at the operating temperature.

Q5: Can this equation be used for turbulent flow?
A: No, for turbulent flow conditions, different equations (such as the Darcy-Weisbach equation) must be used.