A tank with a small circular hole contains oil on top of water . It is immersed in a larger tank of the same oil . Water flows through the hole .
(a) What is the velocity of this flow intially ?
(b) When the flows stops , what would be the position of the oil - water interface in the tank ? (density of oil = 8 gm/cc)

Explanation

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 .