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A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm2 area forms at the bottom of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due to gravity to be 10 m/s2, the rate of leakage of water (in litre/min) through the hole from the tank to the atmosphere, under the given conditions, is _______
(Important - Enter only the numerical value in the answer)
Correct answer is '3'. Can you explain this answer?
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Given data:
Diameter of the tank (D) = 1 m
Height of the water (h) = 5 m
Area of the hole (A) = 5 mm^2 = 5 × 10^-6 m^2
Coefficient of discharge (Cd) = 1
Acceleration due to gravity (g) = 10 m/s^2
To find:
Rate of leakage of water through the hole (in liters/min)
Formula:
The rate of leakage of water through the hole can be calculated using Torricelli's law, which states that the velocity of efflux (v) is given by the equation:
v = sqrt(2gh)
where v is the velocity of efflux, g is the acceleration due to gravity, and h is the height of the water column above the hole.
The rate of leakage (Q) is given by the equation:
Q = Av
where A is the area of the hole.
Calculation:
1. Calculate the velocity of efflux using Torricelli's law:
v = sqrt(2gh)
= sqrt(2 × 10 × 5)
= 10 m/s
2. Calculate the rate of leakage using the formula:
Q = Av
= (5 × 10^-6) × 10
= 5 × 10^-5 m^3/s
3. Convert the rate of leakage from m^3/s to liters/min:
1 m^3 = 1000 liters
1 s = 60 seconds
1 minute = 60 seconds
Q = (5 × 10^-5) × (1000 × 60)
= 3 liters/min
Therefore, the rate of leakage of water through the hole from the tank to the atmosphere, under the given conditions, is 3 liters/min.
Diameter of the tank (D) = 1 m
Height of the water (h) = 5 m
Area of the hole (A) = 5 mm^2 = 5 × 10^-6 m^2
Coefficient of discharge (Cd) = 1
Acceleration due to gravity (g) = 10 m/s^2
To find:
Rate of leakage of water through the hole (in liters/min)
Formula:
The rate of leakage of water through the hole can be calculated using Torricelli's law, which states that the velocity of efflux (v) is given by the equation:
v = sqrt(2gh)
where v is the velocity of efflux, g is the acceleration due to gravity, and h is the height of the water column above the hole.
The rate of leakage (Q) is given by the equation:
Q = Av
where A is the area of the hole.
Calculation:
1. Calculate the velocity of efflux using Torricelli's law:
v = sqrt(2gh)
= sqrt(2 × 10 × 5)
= 10 m/s
2. Calculate the rate of leakage using the formula:
Q = Av
= (5 × 10^-6) × 10
= 5 × 10^-5 m^3/s
3. Convert the rate of leakage from m^3/s to liters/min:
1 m^3 = 1000 liters
1 s = 60 seconds
1 minute = 60 seconds
Q = (5 × 10^-5) × (1000 × 60)
= 3 liters/min
Therefore, the rate of leakage of water through the hole from the tank to the atmosphere, under the given conditions, is 3 liters/min.
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A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from itsbottom. Top surface of water is exposed to atmosphere. A hole of 5 mm2 area forms at thebottom of the tank. Considering the coefficient of discharge of the hole to be unity and theacceleration due to gravity to be 10 m/s2, the rate of leakage of water (in litre/min) through thehole from the tank to the atmosphere, under the given conditions, is _______(Important - Enter only the numerical value in the answer)Correct answer is '3'. Can you explain this answer?
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