Water flows through the tube shown in figure. The areas of cross section of the wide and the narrow portions of the tube are `5cm^2 and 2cm^2` respectively. The rate of flow of water through the tube is `500 cm^3s^-1` . Find the difference of mercury levels in the U-tube.

Explanation

`a_1 = 5 cm^2, a_2 = 2 cm^2`, rate of flow `Q = 500 cm^3//s`
`Q = a_1 v_1 = a_2 v_2`
`500 = 5 v_1 = 2 v_2`
`v_1 = 100 cm//s,v_2 = 250 cm//s`
`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) = (1)/(2) xx 1 xx(150^2 - 100^2)`
=`26,250 "dyne"//cm^2`
Let this pressure difference corresponds to `h cm` of mercury
`rho_m gh = P_1 - P_2`
`13.6 xx 980 h = 26,250`
`h = 1.97 cm`.
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