Calculate the time taken to completely empty aswimming pool 15
m long and 9 m wide through an opening at thebottom as shown in the
fig. the swimming pool holds water to depth1.5 m. opening area is
0.3 sq. m and cd=0.62.

Time needed to empty the pool is 401.35 seconds.

Explanation:

The exit velocity of the water from the orifice is obtained from the Torricelli's law as

where

'h' is the head under which the flow of water occurs

Thus the theoretical discharge through the orifice equals

Now we know that

Thus using this relation we obtain

Now we know by definition of discharge

Using the above relations we obtain

The limits are put that at time t = 0 height in pool = 1.5 m and at time 't' the height in pool = 0

Solving for 't' we get