Pressure Calculation From Flow Rate

Hagen-Poiseuille Equation:

\[ P = \frac{8 \mu L Q}{\pi r^4} \]

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

m³/s

Radius (r):

Pressure (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 in laminar flow through a long cylindrical pipe of constant cross section. It provides a mathematical relationship between pressure difference, flow rate, and fluid properties.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ P = \frac{8 \mu L Q}{\pi r^4} \]

Where:

\( P \) — Pressure (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Length of pipe (m)
\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Radius of pipe (m)

Explanation: The equation shows that pressure drop is directly proportional to viscosity, length, and flow rate, and inversely proportional to the fourth power of the radius.

3. Importance of Pressure Calculation

Details: Accurate pressure calculation is crucial for designing fluid systems, determining pump requirements, and ensuring proper flow in various engineering applications including plumbing, HVAC systems, and medical devices.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure all values are positive and non-zero. The radius is particularly sensitive as it's raised to the fourth power in the calculation.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of the Hagen-Poiseuille equation?
A: It assumes laminar flow, Newtonian fluid, constant cross-section, no-slip condition, and no end effects. It's not valid for turbulent flow or non-Newtonian fluids.

Q2: How does pipe roughness affect the calculation?
A: The equation assumes smooth pipes. For rough pipes, additional friction factors need to be considered, especially in turbulent flow conditions.

Q3: What is the Reynolds number range for valid application?
A: The equation is valid for Reynolds numbers below approximately 2300, where flow is laminar.

Q4: Can this be used for non-circular pipes?
A: No, the equation is specifically for circular cross-sections. For non-circular pipes, the hydraulic diameter concept must be used with appropriate corrections.

Q5: How does temperature affect the calculation?
A: Temperature significantly affects viscosity. For accurate calculations, use viscosity values at the operating temperature of the fluid.