Pressure Calculator for Water Flow Rate

Pressure Difference Formula:

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

Water Viscosity (μ):

Pa·s

Pipe Length (L):

Flow Rate (Q):

m³/s

Pipe Radius (r):

Pressure Difference (ΔP):

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1. What is a Pressure Calculator for Water Flow Rate?

Definition: This calculator determines the pressure difference required to maintain a specific water flow rate through a pipe using the Hagen-Poiseuille equation.

Purpose: It helps engineers and plumbers design fluid systems by calculating the pressure needed for desired flow rates.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

\( \Delta P \) — Pressure difference (Pascals)
\( \mu \) — Dynamic viscosity of water (Pa·s)
\( L \) — Length of the pipe (meters)
\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Pipe radius (meters)

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

3. Importance of Pressure Calculation

Details: Accurate pressure calculations ensure proper pump selection, prevent pipe damage, and maintain desired flow rates in fluid systems.

4. Using the Calculator

Tips: Enter water viscosity (default 0.001002 Pa·s for water at 20°C), pipe length, flow rate, and pipe radius. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical viscosity of water?
A: At 20°C (68°F), water has a viscosity of about 0.001002 Pa·s. This changes with temperature.

Q2: Why does radius have such a large effect?
A: The r⁴ term means doubling the radius reduces the required pressure by a factor of 16 for the same flow rate.

Q3: Does this work for any fluid?
A: The equation works for laminar flow of Newtonian fluids in circular pipes. Adjust viscosity for different fluids.

Q4: What about turbulent flow?
A: This calculator assumes laminar flow (Re < 2100). For turbulent flow, different equations apply.

Q5: How do I convert between units?
A: 1 Pa = 1 N/m² = 0.000145 psi. 1 m³/s = 15850.3 gallons per minute (gpm).