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.

Answer

A, C

Explanation

Applying continuty equation
`A_(1)v_(1)=A_(2)v_(2)`=rate to flow of water
` 5v_(1)=2v_(2)=500cm^(2)//s`
`:. v_(1)=100cm//s=1.0 m//s`
`v_(2)=250 cm//s=2.5 m//s`
Now, applying Bernoulli's equation at 1 and 2
`p_(1)+(1)/(2) rho_(w)v_(1^(2)+rho_(w)gh_(1)=p_(2)+(1)/(2) rho_(w)v_(2)^(2)+rho_(w)gh_(2) (h_(1) =h_(2))`
`implies (1)/(2) rho_(w)(v_(2)^(2)-v_(1)^(2))=p_(1)-p_(2)=rho_(Hg)gh_(Hg)`
or `(1)/(2) rho_(w)(v_(2)^(2)-v_(1)^(2))=rho_(Hg)gh_(Hg)`
`:. h_(Hg)=(rho_(w)(v_(2)^(2)-v_(1)^(2)))/(2 rho_(Hg) g)`
`=(10^(3)(6.25-1))/(2xx13.6xx10^(3)xx9.8)`
`=0.0196m`
`=1.96 cm`.