Flow rate Q = 200 gal/min = 0.4456 ft3/s

Inlet pipe cross-section Ain = pi/4 * Din2 = 3.14/4 * (4/12)2 = 0.0872 ft2

Discharge pipe cross-section Aout = pi/4 * Dout2 = 3.14/4 * (3/12)2 = 0.0491 ft2

Velocity in inlet pipe V1 = Q / Ain = 0.4456 / 0.0872 = 5.11 ft/s

Velocity in discharge pipe V2 = Q / Aout = 0.4456 / 0.0491 = 9.08 ft/s

For water at 70F, kinematic viscosity, neu = 1.052*10-5 ft2/s

Reynolds number in inlet pipe Re1 = V1*Din / neu = 5.11*(4/12) / (1.052*10-5) = 161917

Reynolds number in discharge pipe Re2 = V2*Dout / neu = 9.08*(3/12) / (1.052*10-5) = 215779

For commercial steel pipe, roughness e = 0.00015 ft

In inlet pipe, relative roughness e/Din = 0.00015 / (4/12) = 0.00045

In discharge pipe, relative roughness e/Dout = 0.00015 / (3/12) = 0.0006

From Moody diagram, for Re1 = 161917 and e/Din = 0.00045, we get friction factor f1 = 0.019

From Moody diagram, for Re2 = 215779 and e/Dout = 0.0006, we get friction factor f2 = 0.0193

For threaded 90 deg elbow, loss coeff K = 1.5

For rounded pipe entrance, K = 0.04

For pipe exit, K = 1

Total inlet pipe length L1 = 10 + 14 = 24 ft

Total discharge pipe length L2 = 14 + 20 + 14 + 14 + (6 - (22-20)/2) = 67 ft

Head at inlet of pump = [15 + V12 / (2g)] - (0.04 + 1.5 + f1*L1/Din) V12 / (2g)

Head at inlet of pump = 15 - (0.04 + 1.5 + 0.019*24/(4/12) - 1) 5.112 / (2*32.2)

Head at inlet of pump = 14.226 ft

Pressure at inlet of pump = 14.226*rho = 14.226*62.4 = 887.72 lb/ft2 = 6.16 psi (gage)....Ans (b)

For the discharge line, 14.226 + Hp - (3*1.5 + 15 + 1 + f2*L2 / Dout)*V22 / (2g) - 22 + 6 = 0 + V22 / (2g)

14.226 + Hp - (3*1.5 + 15 + 1 + f2*L2 / Dout - 1)*V22 / (2g) - 22 + 6 = 0

14.226 + Hp - (3*1.5 + 15 + 1 + 0.0193*67 / (3/12) - 1)*9.082 / (2*32.2) - 22 + 6 = 0

Hp = 33.36 ft............Ans (a)