Pressure Calculator From Flow Rate

Hagen-Poiseuille Equation:

\[ P = \frac{Q \times \rho \times 8 \times L}{\pi^2 \times D^5 \times g} \]

Flow Rate (Q):

m³/s

Density (ρ):

kg/m³

Length (L):

Diameter (D):

Gravity (g):

m/s²

Pressure Drop (P):

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1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the pressure drop in an incompressible Newtonian fluid flowing through a long cylindrical pipe. It provides an approximation for laminar flow conditions and is fundamental in fluid dynamics calculations.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ P = \frac{Q \times \rho \times 8 \times L}{\pi^2 \times D^5 \times g} \]

Where:

\( P \) — Pressure drop (Pa)
\( Q \) — Volumetric flow rate (m³/s)
\( \rho \) — Fluid density (kg/m³)
\( L \) — Pipe length (m)
\( D \) — Pipe diameter (m)
\( g \) — Gravitational acceleration (m/s²)

Explanation: The equation calculates the pressure difference required to maintain a given flow rate through a pipe of specified dimensions, considering fluid properties and gravitational effects.

3. Importance of Pressure Drop Calculation

Details: Accurate pressure drop calculation is crucial for designing piping systems, selecting appropriate pumps, optimizing energy consumption, and ensuring proper fluid transport in various engineering applications.

4. Using the Calculator

Tips: Enter flow rate in m³/s, density in kg/m³, length and diameter in meters, and gravity in m/s². All values must be positive and non-zero. Standard gravity is 9.81 m/s².

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of the Hagen-Poiseuille equation?
A: It assumes laminar flow (Re < 2000), incompressible Newtonian fluids, steady flow, and no-slip boundary conditions. Not suitable for turbulent flow or non-Newtonian fluids.

Q2: How does pipe diameter affect pressure drop?
A: Pressure drop is inversely proportional to the fifth power of diameter. Small changes in diameter significantly impact pressure requirements.

Q3: What is the typical range for flow rates in pipes?
A: Depends on application, but generally 0.001-10 m³/s for most industrial and domestic piping systems.

Q4: When should I use this equation?
A: For laminar flow conditions in circular pipes with constant cross-section. For turbulent flow, use Darcy-Weisbach equation.

Q5: How accurate is this approximation?
A: Very accurate for ideal laminar flow conditions. Accuracy decreases with flow disturbances, pipe roughness, and non-ideal conditions.