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A tank having a small circular hole cont...

A tank having a small circular hole contains oil on top of water. It is immersed in a large tank of the same oil. Water flows through the hole. What is the velocity of the velocity of this flow initially? When the flow stops. What would be the position of the oil-water interface in the tank from the bottom. The specfic gravity of oil is 0.5.

Text Solution

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Applying Bernoulli.s equation between points 1 and 2
` rArr P_(atm) +eho_(0)gh_(0) + rho_(w)gh_(w) = P_(atm) +rho_(0)g(h_(0)+h_(w))+1/2 rho_(w) v^(2)`
`rArr 1/2 rho_(w)v^(2) = gh_(w) (rho_(w) - rho_(0))`
` rArr v = sqrt(2gh_(w)(1- (rho_(0))/(rho_(w)))) = sqrt(2 xx 9.8 xx 10/100 (1- (800)/1000))`
` = 0.63 ` m/s
(b) In the terms of the height h of oil water interface
` P_(atm) +rho_(0)g xx 5 + rho_(w)gh = P_(atm) +rho_(0)g (10+5) +1/2 rho_(w) v^(2)`
` rArr 1/2 rho_(w)v^(2) = g (rho_(w)h - rho_(n).10)`
Flow stops when `rho _(w)h - rho_(o) xx 10 `
` :. h = 0.8 xx10 = 8 cm `
` :. ` The interface is at a height 8 cm above the base .
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