Water Pressure and Pipe Size Calculator (Poiseuille)

Pressure Drop Formula:

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

Viscosity (μ):

Pa·s

Pipe Length (L):

Flow Rate (Q):

m³/s

Pipe Radius (r):

Pressure Drop (ΔP):

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1. What is the Water Pressure and Pipe Size Calculator?

Definition: This calculator estimates the pressure drop in a pipe using Poiseuille's law based on fluid viscosity, pipe length, flow rate, and pipe radius.

Purpose: It helps engineers and plumbers determine pressure losses in piping systems for proper system design and troubleshooting.

2. How Does the Calculator Work?

The calculator uses Poiseuille's law formula:

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

Where:

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

Explanation: The formula calculates the pressure difference needed to maintain a given flow rate in a pipe of specified dimensions.

3. Importance of Pressure Drop Calculation

Details: Proper pressure drop estimation ensures adequate pump sizing, efficient system operation, and prevents flow-related issues in piping systems.

4. Using the Calculator

Tips: Enter the fluid 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's the typical viscosity of water?
A: Water at 20°C has a viscosity of about 0.001002 Pa·s. This changes with temperature.

Q2: How does pipe radius affect pressure drop?
A: Pressure drop is inversely proportional to the fourth power of radius - small radius changes have large effects.

Q3: What units should I use?
A: Use consistent SI units: meters for length/radius, m³/s for flow, Pa·s for viscosity.

Q4: Does this work for turbulent flow?
A: No, Poiseuille's law applies only to laminar flow (Re < 2000 typically).

Q5: How do I convert to other pressure units?
A: 101325 Pa = 1 atm, 6895 Pa = 1 psi. Multiply result by conversion factor.