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Pipeflow Type 2 Application

Example Water flows from a reservoir which is open to the air. The elevation, H, of the surface is 80 ft above the exit through a galvanized iron pipe with diameter of 1/6 ft. Assume a minor loss occurs at the entrance to the pipe is K = 0.5. Neglect the minor loss at the pipe exit. Length, L,

of the pipe is 100 ft. Find the discharge, Q, from the pipe into the open atmosphere.

Strategy: Start by writing the energy equation between stations 1 and 2 and examining the unknowns.

Use this energy equation and the Moody Chart to determine the friction factor, f. Then start the

iteration by assuming a large Reynolds Number (turbulent flow) and use the relative roughness,

e/D, to get the first value of the friction factor from the Moody Chart. Then use the energy

equation to obtain the initial value of fluid velocity at station 2 . Use this velocity to find a new

value for the Reynolds Number and iterate until the change in friction factor is small. Then use

the energy equation again to find the final value of fluid velocity, V₂. The discharge is then the

product of exit velocity time the area of the pipe.

Write the energy equation between stations 1 and 2 in terms of head (ft).

P₁/ρg + V₁²/2g + z₁ = P₂/ρg + V₂²/2g + z₂ + Head Loss from 1 to 2

Head Loss from 1 to 2 = f(L/D) V₂²/2g + K ) V₂²/2g = [f(L/D) + K )] V₂²/2g

Here P₁ = P₂ = 0 psig z₁ = 80 ft z₂ = 0 ft (datum) V₁ ~ 0 (large tank)

z₁ = V₂²/2g + [f(L/D) + K )] V₂²/2g = [ 1 + [f(L/D) + K )] V₂²/2g (ft) (1)

The unknowns are: f and V₂ so iteration will be required to find the discharge, Q.

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