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Solution
Answer: B) 161 psi
Refer to PE Civil Reference Handbook Section 6.3.1.3:
Circular Pipe Head Loss (as pressure)
\[P=\frac{(4.52Q^{1.85})}{(C^{1.85} D^{4.87} )}\]
where:
\(P = Pressure\ Loss\ (psi\ per\ linear\ foot)\)
\(Q = Flow (gpm) = V\times A\)
\[Q = \pi /4 \times (8 \ in/12)^2 \times 7 ft/s= 2.443ft^3/sec = 2.443 \times 448.83 = 1096.5\ gpm \\\]\(D = Pipe \ Diameter \ (in)\)
\(C=\text{Hazen-Williams coefficient, refer to the table Handbook Section 6.3.1.4:}\)
\[C= 100 (20 \ \text{years old cast iron pipe})\]
\[P= \frac{4.52\times(1096.5)^{1.85}}{100^{1.85}\times 8^{4.87}} =0.01516\ psi /ft\\\]
Total Pressure Loss:
\[0.01516 \ psi/ft\times 4000 ft = 60.65\ psi\]
Appling the Bernoulli Equation at inlet and outlet:
- The velocity term is canceled because the pipe has same cross section along its length.
- The elevation term is canceled as the pipe is horizontal (no elevation difference).
\[P_{inlet} = P_{outlet} + Losses = 100 \ psi +60.65 \ psi= 160.65\ psi\\\]
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