Answer to Question #278937 in Classical Mechanics for joseph

Question

1. The maximum flow rate in an 8-in. diameter (horizontal) waterline is 4.3 cfs. If a 4-in. Venturi meter is installed in the pipe to measure flow, estimate the necessary length of a vertical U-tube scale for the differential water-mercury (SG = 13.6) manometer.

2. A 50-cm diameter (horizontal) pipe contains a 20-cm Venturi meter. Determine the flow rate if the pressure difference reading between the throat and entry section in a water-mercury (SG = 13.6) manometer is 1.46 m.

Answer 1

$a_1=0 25\pi d_1^2=0.196~m^2,$

$a_2=0 25\pi d_2^2=0.031~m^2,$

$Q=\frac{a_1a_2}{\sqrt{a_1^2-a_2^2}}\sqrt{2gh}=1.17~\frac{m^3}s.$