A venturi meter is used to measure the flow speed of a fluid in a pipe . The meter is connected between two sections of the pipe (Fig) the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area a with speed v . A manometer connects the wider portion of the meter to the narrower portion . The change in the fluid's speed is accompanied by a change `Deltap` in the fluid 's pressure , which causes a height difference h of the liquid in the two arms of the manometer. (Here , `Deltap` means pressure in the throat minus pressure in the pipe).

Suppose that the fluid is fresh water , that the cross-sectional areas are `64 cm^(2)` in the pipe and `32 cm^(2)` in the throat , and that the pressure is 55 kPa in the pipe and 41 kPa in the throat , and that the pressure is 55 kPa in the pipe and 41 kPa in the throat . What is the rate of water flow in cubic meters per second ?

Explanation

We substitute the values to obtain
`v = sqrt((2 (32 xx 10^(-4) m^(2))^(2) [(55 xx 10^(3) Pa) - (41 xx 10^(3) Pa)])/((1000 kg //m^(3))[(64 xx 10^(-4) m^(2))^(2) - (32 xx 10^-4 m^(2) )^(2)])`
Consequently , the flow rate is
`Av = (64 xx 10^(-4) m^(2)) (3.06 m//s) = 2.0 xx 10^(-2) m^(3)//s`