An open cylinder of height 5ft and cross sectional area of 1 ft2 is initially empty. There is a small hole at the bottom of the cylinder with an area of 0.005 ft2. Water is drawn into the tank at a rate of 4.8ft3/min. At the same time water is discharged out of the cylinder through a small hole at the bottom of the tank. The outlet velocity may be estimated from Torricelli’s theorem. Estimate the time required for the water level in the tank to reach one foot depth.
dVolume/dTime = -a(2gy)^(1/2)
The Attempt at a Solution
I tried to solve this by Torricelli's Law and setting up a model that :
Volume of water remain in tank = Volume water in-volume water out
But I found that time need for water level in tank = 1 foot is only 0.21 second
I think the model is wrong, please help me with the model.