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Gravity Flow Rate Calculator - Hazen Williams equation Calculator

Gravity Flow Rate Calculator
Material Roughness coefficient

Material Roughness Coefficients

Material Roughness Coefficient
Cast Iron 100
Concrete 110
Copper 140
Plastic 150
Steel 120

Velocity of Water Flow in a Pipe: An Example


Let’s use the pipe flow calculator to determine the velocity and discharge of a plastic pipe with a diameter of 0.6 feet. The pipe is 15 feet long, and the height difference between the beginning and endpoints is 6 feet.


Step-by-Step Calculation:
1. Calculate the Radius of the Pipe

Divide the diameter by 2 to find the radius:

\[ r = \frac{d}{2} = \frac{0.6}{2} = 0.3 \, \text{ft} \]

2. Find the Cross-Sectional Area of the Pipe

Use the formula for the area of a circle:

\[ A = \pi r^2 = \pi \times 0.3^2 \approx 0.2827 \, \text{ft}^2 \]

3. Determine the Perimeter of the Pipe

Calculate the perimeter using the formula:

\[ P = 2 \pi r = 2 \pi \times 0.3 \approx 1.885 \, \text{ft} \]

4. Calculate the Hydraulic Radius

Divide the area by the perimeter:

\[ R = \frac{A}{P} = \frac{0.2827}{1.885} \approx 0.15 \, \text{ft} \]

5. Select the Roughness Coefficient

Choose "Plastic" from the drop-down list, which has a roughness coefficient of:

\[ C = 150 \]

6. Calculate the Slope of the Pipe

Divide the height difference by the length of the pipe:

\[ S = \frac{y}{L} = \frac{6}{15} = 0.4 \]

7. Use the Hazen-Williams Equation to Find Velocity

Apply the Hazen-Williams formula:

\[ v = 1.318 \times C \times R^{0.63} \times S^{0.54} \]

\[ v = 1.318 \times 150 \times 0.15^{0.63} \times 0.4^{0.54} \approx 36.48 \, \text{ft/s} \]

8. Calculate the Discharge

Multiply the velocity by the cross-sectional area:

\[ Q = A \times v = 0.2827 \times 34.56 \approx 10.31 \, \text{ft}^3/\text{s} \]

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