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A cylindrical tank is filled with water ...

A cylindrical tank is filled with water to a level of 4 m. A hole is opened at a height of 60 cm from bottom. The ratio of the area of the hole to that at cross-sectinal area at cylinder is `0.2.` Then the velocity with which water is coming out is `(g = 10m//s^(2))`

A

The speed with which water level decreases is `V = (a v_e)/(A )` where `v_e` is the velocity of efflux.

B

The velocity of efflux is equal to 50 m/s.

C

The speed with which water level decreases is ` V = (a)/(Av_e)` where `v_e` is the velocity of efflux.

D

The velocity of efflux is equal to 7.07 m/s.

Text Solution

Verified by Experts

The correct Answer is:
A, D
According to equation of continuity
av = constant
According to Bernoulli.s theorem
` P + rho gh + 1/2 rho v^2 ` = constant
Applying Bernoulli.s theorem and equation of continuity for the stated case.
Let` v_e` be the velocity of efflux and V be the speed with which level decreases. So, `av_2 = A.V or, V = (av_e)/(A)` ...(i)
Where a is the area of hole and A is the area of cross section of tank
So , `rho_0 + Hrho g + 1/2 rho [ (av_e)/(A)]^2 = rho_0 + 1/2 rho v_e^2`
`v_e^2 = (2Hg)/(1- (a/A)^2) = (2 xx (3 - 0.525) xx 10)/(1 - (0.1)^2)`
` v_e^2 = 50 m^2//s^2 rArr v_e = 7.07 m//s `
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