Discharge from an orifice of 75mm diameter is 002 m3s under

Discharge from an orifice of 75mm diameter is 0.02 m^3/s under a constant head of 3 m. An external mouthpiece of the same diameter is installed that raises the coefficient of contraction from 0.63 to 1.0. The coefficient of velocity is not known and remains unchanged. Determine discharge from the mouthpiece.

Solution

Q = Cd * A * sqrt(2 * g *h)

Cd = Cv * Cc

Q = Cv * Cc * A * sqrt(2 * g *h)

without mouthpiece

0.02 = Cv * 0.63 * pi * 0.075^2 * sqrt(2 * 9.8 * 3) / 4

with mouthpiece

Q = Cv * 1 * pi * 0.075^2 * sqrt(2 * 9.8 * 3) / 4

divide both equations

0.02 / Q   = 0.63 / 1

Q   = 0.031746 m^3/s