Bernoulli's Theorem: Solving a Tank Oil-Water Flow Problem in 32 Seconds

[zorro]

Homework Statement

A tank with 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. The ratio of the cross sectional area of tank to that of hole is 50. The density of oil is 800 Kg/m^3. Find
1)The velocity of water flow
2)When the flow stops, the position of the oil water interface in the tank?
3)The time at which the flow stop

Homework Equations

The Attempt at a Solution

I got the first 2 answers as 6.3m/s and height of water left = 8m respectively
I tried to solve last and got 16 s (app.) but that is wrong.
The answer is 32 s

 

[Mindscrape]

If you show some work then we will be able to show you where you have gone wrong. Nice English by the way.

 

[zorro]

Height of water left after the flow stops = 8 m
Decrease in water level = 2m
volume of water lost = 2 x A (A= area of cross section of the tank)

from the 1st part, velocity of flow=6.3 m/s
volume flowing per second= 6.3 x a (where a is the area of cross section of the hole)

6.3 x a x t= 2 x A
t= 2/6.3 x 50
t=16s (app)

 

[rl.bhat]

The velocity of flow of water does not remain constant. It changes from 6.3 to zero.

 

[zorro]

I got it. Thanks!