Water flows through a horizontal tube as shown in figure. If the difference of heights of water colun in the vertical tubes is 2 cm and the area of cross section at A and B are `4cm^2 and 2cm^2` respectively, find the rate of flow of water across any section.

Explanation

`a_1 = 4 cm^2, a_2 = 2 cm^2`
Continuity equation : `a_1 v_1 = a_2 v_2`
`4 v_1 = 2v_2 rArr v_2 = 2 v_1`
Bernoulli's equation : `P_1 + (1)/(2) rho v_1^2 = P_2 + (1)/(2) rho v_2^2`
`P_1 - P_2= (1)/(2)rho (v_2^2 -v_1^2)`
`rho gh = (1)/(2)rho(4v_2^2 - v_1^2)`
`v_1 = sqrt((2 gh)/(3)) = sqrt((2 xx 1000 xx 2)/(3)) = 36.5 cm//s`
Rate of flow `Q = a_1 v_1 = 4 xx 36.5 = 146 cm^3//s`.
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