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When a tap is closed, the manometer atta...

When a tap is closed, the manometer attached to the pipe reads `3.5xx10^(5)Nm^(-2)`. When the tap is opened, the reading of manometer falls to `3.0xx10^(5)Nm^(-2)`. The velocity of water in the pipe is

A

`100ms^(-1)`

B

`10ms^(-1)`

C

`1ms^(-1)`

D

`10sqrt(10)ms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Bernoulli's theorem for unit mass of liquid,
`(p)/(rho)+(1)/(2)v^(2)=`constant
As the liquid starts flowing, it pressure energy decreases
`(1)/(2)v^(2)=(p_(1)-p_(2))/(rho)`
`implies(1)/(2)v^(2)=(3.5xx10^(5)-3xx10^(5))/(10^(3))`
`impliesv^(2)=(2xx0.5xx10^(5))/(10^(3))`
or `v^(2)=100impliesv=10ms^(-1)`.
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