Agilent Pressure Flow Calculator Formula

Poiseuille's Law:

\[ P = \frac{8 \times \eta \times L \times F}{\pi \times r^4} \]

Viscosity (η):

Pa·s

Length (L):

Flow (F):

m³/s

Radius (r):

Pressure (P):

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1. What is Poiseuille's Law?

Poiseuille's Law describes the pressure drop in an incompressible Newtonian fluid in laminar flow through a long cylindrical pipe. It provides a mathematical relationship between pressure, flow rate, and the physical properties of the fluid and pipe.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law equation:

\[ P = \frac{8 \times \eta \times L \times F}{\pi \times r^4} \]

Where:

\( P \) — Pressure (Pa)
\( \eta \) — Viscosity (Pa·s)
\( L \) — Length of pipe (m)
\( F \) — Flow rate (m³/s)
\( r \) — Radius of pipe (m)

Explanation: The equation shows that pressure 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, optimizing pipe dimensions, and ensuring proper fluid delivery 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 numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Poiseuille's Law?
A: The law assumes laminar flow, Newtonian fluid, constant viscosity, no slip at the pipe wall, and a long straight pipe with constant circular cross-section.

Q2: How does radius affect pressure requirements?
A: Since pressure is inversely proportional to r⁴, small changes in radius significantly affect pressure requirements. Halving the radius increases pressure requirement by 16 times.

Q3: What is a typical viscosity range for common fluids?
A: Water: ~0.001 Pa·s, Air: ~0.000018 Pa·s, Honey: ~10 Pa·s, Motor oil: ~0.1-1 Pa·s (varies with temperature and grade).

Q4: When is Poiseuille's Law not applicable?
A: Not applicable for turbulent flow, non-Newtonian fluids, short pipes, pipes with bends or obstructions, or compressible fluids.

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.