Water Flow Rate Pressure Calculator

Hagen-Poiseuille Equation:

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

Pipe Radius (r):

Pressure Difference (ΔP):

Dynamic Viscosity (μ):

Pa·s

Pipe Length (L):

Flow Rate (Q): m³/s

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1. What is a Water Flow Rate Pressure Calculator?

Definition: This calculator determines the volumetric flow rate of water through a pipe using the Hagen-Poiseuille equation.

Purpose: It helps engineers and fluid dynamics professionals calculate laminar flow rates in pipes based on pressure differences and pipe characteristics.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

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 equation describes laminar flow through a cylindrical pipe, showing that flow rate is proportional to the fourth power of the radius and the pressure difference.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are essential for designing piping systems, predicting fluid behavior, and ensuring proper system performance in applications like plumbing, HVAC, and industrial processes.

4. Using the Calculator

Tips: Enter the pipe radius (in meters), pressure difference (in Pascals), dynamic viscosity (default 0.001002 Pa·s for water at 20°C), and pipe length (in meters). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this equation?
A: The Hagen-Poiseuille equation is valid for steady, laminar flow (Re < 2100) in long, straight pipes with constant circular cross-section.

Q2: What's the typical viscosity value for water?
A: At 20°C, water has a dynamic viscosity of about 0.001002 Pa·s. This decreases with increasing temperature.

Q3: Why does radius have such a large effect (r⁴)?
A: The r⁴ relationship means small changes in pipe diameter dramatically affect flow rate, which is why larger pipes can carry much more fluid.

Q4: How does pipe length affect flow rate?
A: Flow rate is inversely proportional to pipe length - longer pipes have greater resistance, reducing flow for a given pressure difference.

Q5: What if my flow is turbulent?
A: For turbulent flow (Re > 4000), you would need to use the Darcy-Weisbach equation instead, which accounts for friction factors.