Practice Question: Head Loss Due to Friction (Hazen-Williams)

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Solution

Answer: A) 22.5 psi

Pressure drop in a pipe can be determined by its relation to head loss.
$$ \Delta p=p_{in}-p_{out} $$

Using the Hazen-Williams equation, we can determine the approximate head loss:

\[P=\frac{4.52\ast L\ast Q^{1.85}}{C^{1.85}\ast d^{4.87}}\]Reference Section 6.3.1.3 from PE Civil Handbook. Equation was modified to consider length of pipe since original equation from handbook yields pressure loss per unit of length.
where:
$$ L=length\ of\ pipe\ \left(feet\right)=300\ ft $$
$$ Q=flow\ \left(gallons\ per\ minute\right)=4500\ gpm $$
$$ C=roughness\ coefficient\ \ \left(unitless\right)=130 $$
$$ d=diameter\ of\ pipe\ \left(inches\right)=14\ in $$

\[p_{in}-20\ psi=\frac{4.52\ast(300\ ft)\ast{(4500\ gpm)}^{1.85}}{{(130)}^{1.85}\ast\left(14\ in\right)^{4.87}}\]\[p_{in}=22.5\ psi\]

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