Water Velocity Calculator

Calculate the velocity of water flowing through a pipe based on flow rate and pipe diameter. Essential for plumbing system design and hydraulic calculations.

Calculate Water Velocity

Understanding Water Velocity in Pipes

Water velocity calculation is fundamental in hydraulic engineering and fluid mechanics. This guide explains how to determine the velocity of water flowing through a pipe based on flow rate and pipe dimensions.

Water Velocity Formula

The velocity of water in a pipe is calculated using the continuity equation:

\[ v = \frac{Q}{A} = \frac{4Q}{\pi D^2} \]

Where:

  • v = Water velocity (feet per second, ft/s)
  • Q = Flow rate (cubic feet per second, ft³/s)
  • A = Cross-sectional area of pipe (square feet, ft²)
  • D = Inner diameter of pipe (feet)
  • π = Pi (approximately 3.14159)

The Reynolds number can be calculated using:

\[ Re = \frac{vD}{\nu} \]

Where:

  • Re = Reynolds number (dimensionless)
  • v = Velocity (ft/s)
  • D = Pipe diameter (ft)
  • ν = Kinematic viscosity of water (≈ 1.0 × 10⁻⁵ ft²/s at 68°F)

Calculation Steps

  1. Convert all measurements to consistent units (feet and seconds)
  2. Calculate the pipe's cross-sectional area using A = πD²/4
  3. Apply the velocity formula: v = Q/A
  4. Calculate Reynolds number to determine flow characteristics

Example Calculation

Problem:

Calculate the water velocity and Reynolds number for:

  • Flow rate = 100 gallons per minute (GPM)
  • Pipe diameter = 2 inches

Solution:

  1. Convert units:
    Flow rate: \[ 100 \text{ GPM} = \frac{100 \times 0.133681}{60} = 0.223 \text{ ft}^3\text{/s} \]
    Diameter: \[ 2 \text{ inches} = \frac{2}{12} = 0.167 \text{ ft} \]
  2. Calculate area: \[ A = \frac{\pi (0.167)^2}{4} = 0.0219 \text{ ft}^2 \]
  3. Calculate velocity: \[ v = \frac{0.223}{0.0219} = 10.18 \text{ ft/s} \]
  4. Calculate Reynolds number: \[ Re = \frac{10.18 \times 0.167}{1.0 \times 10^{-5}} = 169,803 \]

Since Re > 4000, this indicates turbulent flow.

Flow Visualization

Pipe Diameter Flow Direction Cross Section Side View

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