Pressure vs Flow Rate Calculator

Poiseuille's Law Formula:

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

Radius (r):

meters

Pressure Difference (ΔP):

Viscosity (μ):

Pa·s

Length (L):

meters

Flow Rate (Q):

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1. What is a Pressure vs Flow Rate Calculator?

Definition: This calculator determines the volumetric flow rate of a fluid through a pipe using Poiseuille's law.

Purpose: It helps engineers and scientists understand the relationship between pressure difference and flow rate in laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses Poiseuille's law formula:

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

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Pipe radius (m)
\( \Delta P \) — Pressure difference (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Pipe length (m)

Explanation: The flow rate is directly proportional to the pressure difference and the fourth power of the radius, and inversely proportional to viscosity and pipe length.

3. Importance of Flow Rate Calculation

Details: Understanding this relationship is crucial for designing fluid systems, predicting flow behavior, and optimizing pipe dimensions in various engineering applications.

4. Using the Calculator

Tips: Enter the pipe radius (in meters), pressure difference (in Pascals), fluid viscosity (default 0.001 Pa·s for water at 20°C), and pipe length (in meters). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Poiseuille's law?
A: It applies only to laminar flow (Re < 2000), Newtonian fluids, and long straight pipes with constant circular cross-section.

Q2: What's a typical viscosity value for water?
A: Water at 20°C has viscosity of about 0.001 Pa·s. The calculator defaults to this value.

Q3: Why does radius have such a strong effect (r⁴)?
A: The flow rate increases dramatically with radius because both the cross-sectional area (r²) and average velocity (also r²) depend on radius.

Q4: Can I use this for gases?
A: Only for very slow flows where compressibility effects are negligible. For most gas flows, more complex equations are needed.

Q5: How does temperature affect the calculation?
A: Temperature primarily affects viscosity. For water, viscosity decreases by about 2% per °C temperature increase.