• Diameter of the cylindrical tank = 2 m


• Depth of water in the tank = 3 m


• Diameter of the orifice = 5 cm

The volume of water in the tank can be calculated using the formula for the volume of a cylinder:

V = πr^2h

Where:
V = volume of water in the tank
π = 3.14 (approximate value of pi)
r = radius of the tank = diameter/2 = 2/2 = 1 m
h = depth of water in the tank = 3 m

Substituting the values into the formula, we get:

V = 3.14 * 1^2 * 3
V = 9.42 cubic meters

Therefore, the initial volume of water in the tank is 9.42 cubic meters.


The cross-sectional area of the orifice can be calculated using the formula for the area of a circle:

A = πr^2

Where:
A = cross-sectional area of the orifice
π = 3.14 (approximate value of pi)
r = radius of the orifice = diameter/2 = 5/200 = 0.025 m

Substituting the values into the formula, we get:

A = 3.14 * (0.025)^2
A = 0.00196 square meters

Therefore, the cross-sectional area of the orifice is 0.00196 square meters.


The flow rate of water through the orifice can be calculated using Torricelli's law:

Q = A * √(2gh)

Where:
Q = flow rate of water
A = cross-sectional area of the orifice
g = acceleration due to gravity = 9.81 m/s^2
h = depth of water above the orifice

Substituting the values into the formula, we get:

Q = 0.00196 * √(2 * 9.81 * 3)
Q = 0.00196 * √58.86
Q = 0.00196 * 7.67
Q ≈ 0.01507 cubic meters per second

Therefore, the flow rate of water through the orifice is approximately 0.01507 cubic meters per second.


The time required to empty the tank can be calculated by dividing the initial volume of water in the tank by the flow rate of water through the orifice:

t = V / Q
t = 9.42 / 0.01507
t ≈ 625.08 seconds

Therefore, the time required to empty the tank is approximately 625.08 seconds or 10.42 minutes.


The time required to empty a cylindrical tank with a 2 m diameter and filled with water for a depth of 3 m through

340 sec