Practice Question: Pressure Head Using Hazen-Williams Equation

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Solution

Solution: A) 25.5 ft

Calculate the hydraulic radius (R):

Apply the Hazen-Williams equation:

 

where:

 

Calculate the hydraulic slope (S):

Where:

 

Solve for velocity (V):

Calculate the pressure head at the exit (hf out):

where:

Calculate head loss due to friction using the Darcy-Weisbach equation:

where:

 

For turbulent flow in smooth pipes, we can use the Moody diagram to estimate the friction factor (f) based on Reynolds number (Re) and relative roughness (ε/D). Assuming Re is high enough for turbulent flow, you can find f ≈ 0.015 from a Moody diagram.

Finally, calculate the pressure head at the exit:

Therefore, the pressure head at the pipe exit is approximately

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