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A liquid flows through a horizontal tube...

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 differnece in the levels of the liquid in the two vertical tubes is `h`. then

A

`v_(2)^(2)-v_(1)^(2)=2gh`

B

`v_(2)^(2)+v_(1)^(2)=2gh`

C

`v_(2)^(2)-v_(1)^(2)=gh`

D

`v_(2)^(2)+v_(1)^(2)=gh`

Text Solution

Verified by Experts

The correct Answer is:
A
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 flow of liquid,
`P_(1) +(1)/(2)rhoV_(1)^(2)=P_(2)+(1)/(2)rhov_(2)^(2)`
`P_(1)-P_(2)=(1)/(2)(rhov_(2)^(2)-rhov_(1)^(2))`
`hrhog=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))" "(because P_(1)-P_(2)=hrhog)`
`v_(2)^(2)-v_(1)^(2)=2hg`
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