A liquid flows through a horizontal tube as shown in figure. The velocities of the liquid in the two sections, which have areas of cross-section `A_(1)` and `A_(2)` and `v_(1)` and `v_(2)` respectively. The difference in the levels of the liquid in the two vertical tubes is `h`, then

Options

A. `v_(2)^(2)-v_(1)^(2) = 2 gh`
B. `v_(2)^(2)+v_(1)^(2) = 2 gh`
C. `v_(2)^(2)-v_(1)^(2) = gh`
D. `v_(2)^(2)+v_(1)^(2) = gh`

Answer

A

Explanation

Let `rho` be density of liquid flowing in the tube.
`A_(1)v_(1)=A_(2)v_(2)`
`(v_1)/(v_2) = (A_2)/(A_1)`
According to Bernoulli's equation for horizontal of liquid,
`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)-rho v_(1)^(2))`
`h rho g = 1/2 rho (v_(2)^(2)-v_(1)^(2)) ( :' P_(1)-P_(2)=h rho g`)
`v_(2)^(2)-v_(1)^(2)=2hg`.