A vertical cylindrical tank, 2 m diameter has, at the bottom, a 5
| A vertical cylindrical tank, 2 m diameter has, at the bottom, a 5 cm diameter, sharp-edged orifice, for which Cd =0.6. Water enters the tank at a constant rate of 9l/sec. At what depth above the orifice will the level in the tank become steady?
A. 2.95 m
B. 2.75 m
C. 2.60 m
D. 2.50 m
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Let H be the height at which water level in the tank becomes steady.
At steady state:
Rate at which water enters to tank = Rate at which water flow from orifice = 9 l/sec (given)
Now,
Flow through orifice, \(Q = \;{a_o}{C_d}\sqrt {2gH} \)
Where ; ao = area of orifice
Given: Cd = 0.6, do = 5 cm, Q = 9 l/sec
\(9 \times {10^{ - 3}} = \;\frac{\pi }{4} \times {\left( {0.05} \right)^2} \times 0.6\; \times \sqrt {2 \times 9.81 \times H} \)
On solving, we get
H = 2.96 m
