Pipeline Flow Capacity Calculator

Poiseuille Equation (Laminar Flow):

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

Inner Diameter (ID):

Pressure Drop (ΔP):

Viscosity (μ):

Pa·s

Length (L):

Flow Capacity (Q):

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1. What is the Poiseuille Equation?

The Poiseuille equation describes the flow capacity of a fluid in a pipeline under laminar flow conditions. It provides a mathematical relationship between flow rate, pipe dimensions, fluid properties, and pressure drop.

2. How Does the Calculator Work?

The calculator uses the Poiseuille equation:

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

Where:

\( Q \) — Flow capacity (m³/s)
\( ID \) — 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)

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

3. Importance of Flow Capacity Calculation

Details: Accurate flow capacity calculation is essential for pipeline design, fluid transport systems, hydraulic engineering, and various industrial applications where fluid flow must be precisely controlled and optimized.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When is the Poiseuille equation applicable?
A: The equation is valid for steady, laminar flow of Newtonian fluids in straight, circular pipes with constant cross-section.

Q2: What is the Reynolds number range for laminar flow?
A: Typically, Reynolds number below 2000 indicates laminar flow where Poiseuille's equation applies.

Q3: How does pipe roughness affect the calculation?
A: Poiseuille's equation assumes smooth pipes. For rough pipes, additional friction factors need to be considered.

Q4: Can this equation be used for non-circular pipes?
A: No, the equation is specifically derived for circular cross-sections. Different equations are needed for non-circular conduits.

Q5: What are typical viscosity values for common fluids?
A: Water at 20°C: ~0.001 Pa·s, Air at 20°C: ~0.000018 Pa·s, Engine oil: ~0.1-0.3 Pa·s (varies with temperature and grade).