Head Loss Due to Friction (Hazen-Williams)

Updated to provide proper equation for head loss in pipe.

A new 14-inch diameter welded steel pipe (C = 130), 300 feet in length, is used as a firewater line in an industrial facility.  Given a required outlet pressure of 20 psi and a flow of 750 4500 gallons per minute, calculate the necessary inlet pressure. 

Assume changes in head loss are only due to friction.

A) 22.5 psi

B) 38.6 psi

C) 33.1 psi

D) 27.1 psi


Answer: C) 33.1 psi

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:

\[h_f=\frac{\sout{10.44}\ast L\ast Q^{1.85}}{C^{1.85}\ast d^{4.87}}\]

\[P=\frac{4.52\ast L\ast Q^{1.85}}{C^{1.85}\ast d^{4.87}}\]Reference Section from PE Civil Handbook. Equation was modified to consider length of pipe since original equation from handbook yields pressure loss per unit of length.
$$ L=length\ of\ pipe\ \left(feet\right)=300\ ft $$
$$ Q=flow\ \left(gallons\ per\ minute\right)=750\ gpm $$
$$ C=roughness\ coefficient\ \ \left(unitless\right)=130 $$
$$ d=diameter\ of\ pipe\ \left(inches\right)=14\ in $$

\[p_{in}-20\ psi=\frac{\sout{10.44}\ast(300\ ft)\ast{(\sout{750\ gpm})}^{1.85}}{{(130)}^{1.85}\ast\left(14\ in\right)^{4.87}}\ast\sout{62.4}\frac{lb}{ft^3}\]\[p_{in}-20\ psi=\frac{4.52\ast(300\ ft)\ast{(4500\ gpm)}^{1.85}}{{(130)}^{1.85}\ast\left(14\ in\right)^{4.87}}\]\[\sout{p_{in}=33.1\ psi}\]\[p_{in}=22.5\ psi\]