Flow Rate To Pressure Calculator

Hagen-Poiseuille Equation:

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

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

m³/s

Radius (r):

Pressure Drop (ΔP):

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1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the pressure drop in an incompressible and Newtonian fluid in laminar flow through a long cylindrical pipe. It is fundamental in fluid dynamics for calculating pressure loss due to viscosity.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

\( \Delta P \) — Pressure drop (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Length of the pipe (m)
\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Radius of the pipe (m)
\( \pi \) — Mathematical constant (3.1416)

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 Drop Calculation

Details: Calculating pressure drop is crucial for designing piping systems, determining pump requirements, optimizing fluid transport, and ensuring efficient operation in various engineering applications.

4. Using the Calculator

Tips: Enter viscosity in Pa·s, length in meters, flow rate in m³/s, and radius in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Hagen-Poiseuille equation?
A: The fluid must be Newtonian, incompressible, flow must be laminar, and the pipe must be straight with constant circular cross-section.

Q2: What is the range of validity for this equation?
A: Valid for Reynolds numbers below 2000 (laminar flow regime). For turbulent flow, different equations like Darcy-Weisbach should be used.

Q3: Why is radius to the fourth power so important?
A: The r⁴ term means small changes in radius dramatically affect pressure drop. Doubling the radius reduces pressure drop by a factor of 16.

Q4: What are typical viscosity values for common fluids?
A: Water: ~0.001 Pa·s, Air: ~0.000018 Pa·s, Honey: ~10 Pa·s, Engine Oil: ~0.1-0.3 Pa·s.

Q5: Can this be used for non-circular pipes?
A: No, the equation is specifically for circular pipes. For non-circular conduits, hydraulic diameter concepts must be applied.