A manometer connected to a closed tap reads `3.5xx10^(5)N//m^(2)`.When the valve is opened, the reading of manometer falls to `3.0xx10^(5)N//m^(2)`, then velocity of flow of water is

Options

A. `100 ms ^(-1)`
B. `10 ms ^(-1)`
C. `1 ms ^(-1)`
D. `10 sqrt10 ms ^(-1)`

Answer

B

Explanation

Bernoulli.s theorem for unit mass of liquid is
`(P)/(rho ) + (1)/(2) v ^(2) =` constant
As the liquid starts flowing, its pressure energy decreases
`(1)/(2) v^(2) = (Delta P )/(rho )`
`implies (1)/(2) v ^(2) = ( 3.5 xx 10^(5) - 3 xx 10 ^(5))/( 10 ^(3))`
`implies v ^(2) = (2 xx 0.5 xx 10 ^(5))/(10 ^(3))`
`implies v ^(2) = 100`
`implies v = 10 m//s `