Question

For a discharge of 1.5 cfs, determine the head loss in each component and the total head loss across an entire series pipe system laid out in a horizontal plane, constructed of welded steel pipe, and consisting of the following components arranged in series: 350 ft of 4-inch diameter pipe, a 90° bend, 4-inch gate valve in the fully open position, an additional 60 ft of 4-inch pipe, sudden expansion to 6-inch diameter, 350 ft of 6-inch pipe, sudden contraction to 3-inch diameter, and finally 150 ft of 3-inch diameter pipe discharging into an open top tank having a free surface exposed to atmospheric pressure. Plot both the Energy Grade Line and Hydraulic Grade Line for this series pipe system.

Use the Energy Equation to show that the EGL ordinate, Hx, at any location x along the pipeline is given by Hx = hL(x-fs), where hL(x-fs) is the headloss between location x to the free water surface in the downstream tank. Then, by definition the HGL ordinate, hx, at any location x along the pipeline is given by hx = Hx−(Vx2/2g).

Answer 1

Ans 2) We know, according to Bernoulli equation,

P1/g + V²/2g + x = P2/g + V²/2g + fs + H_L

Pressure and velocity along same plane and cross section remain same, so

H_L = (x - fs)

EGL = pressure head + velocity head + datum head

H_x = 0 + 0 + (x - f_s)

H_x = x - f_s

HGL = EGL - velocity head

= H_x - V²/2g