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A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom. Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice. The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.
Correct answer is '0.52'. Can you explain this answer?
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Verified Answer
A circular water tank of 2 m diameter has a circular orifice of diamet...
Assume H is the level of weter in the tank in steady condition.
For steady water level in the tank
Discharge through orifice = Water enters in the tank
H = 0.5164 m
Most Upvoted Answer
A circular water tank of 2 m diameter has a circular orifice of diamet...
To find the height of the water level in the tank at the steady state, we need to consider the principles of fluid mechanics and apply relevant equations. Let's break down the solution into steps:
Step 1: Calculate the cross-sectional area of the tank
The cross-sectional area of a circular tank can be calculated using the formula: A = πr^2, where r is the radius of the tank. In this case, the diameter of the tank is given as 2 m, so the radius will be 1 m. Therefore, the cross-sectional area is A = π(1^2) = π m^2.
Step 2: Calculate the cross-sectional area of the orifice
Similar to Step 1, we can calculate the cross-sectional area of the orifice using the formula: A = πr^2, where r is the radius of the orifice. Here, the diameter of the orifice is given as 0.1 m, so the radius will be 0.05 m. Therefore, the cross-sectional area of the orifice is A = π(0.05^2) = π(0.0025) = 0.00785 m^2.
Step 3: Convert the flow rate to volume flow rate
The flow rate is given as 20 liters/s. To convert this to a volume flow rate in cubic meters per second, we divide by 1000 (since 1 liter is equal to 0.001 cubic meters). Therefore, the volume flow rate is 20/1000 = 0.02 m^3/s.
Step 4: Apply the equation of continuity
The equation of continuity states that the volume flow rate of a fluid is constant at different cross-sectional areas. Therefore, we can equate the volume flow rate at the tank to the volume flow rate at the orifice:
A_tank * v_tank = A_orifice * v_orifice
Step 5: Calculate the velocity of water at the orifice
Rearranging the equation of continuity, we can solve for the velocity of water at the orifice:
v_orifice = (A_tank * v_tank) / A_orifice
Step 6: Apply the equation for velocity of efflux
The velocity of efflux can be calculated using the equation: v_efflux = √(2gh), where g is the acceleration due to gravity and h is the height of the water level in the tank.
Step 7: Apply the equation for the coefficient of discharge
The coefficient of discharge (Cd) relates the actual discharge to the theoretical discharge. It can be used to modify the equation for velocity of efflux:
v_efflux = Cd * √(2gh)
Step 8: Equate the equations for velocity of efflux and velocity at the orifice
Setting the equations for velocity of efflux and velocity at the orifice equal to each other, we can solve for the height of the water level (h):
Cd * √(2gh) = (A_tank * v_tank) / A_orifice
Step 9: Solve for the height of the water level
Rearranging the equation and plugging in the given values, we can solve for h:
h = [(Cd^2 * (A_tank^2 * v_tank^2)) / (2 * g * A_or
Step 1: Calculate the cross-sectional area of the tank
The cross-sectional area of a circular tank can be calculated using the formula: A = πr^2, where r is the radius of the tank. In this case, the diameter of the tank is given as 2 m, so the radius will be 1 m. Therefore, the cross-sectional area is A = π(1^2) = π m^2.
Step 2: Calculate the cross-sectional area of the orifice
Similar to Step 1, we can calculate the cross-sectional area of the orifice using the formula: A = πr^2, where r is the radius of the orifice. Here, the diameter of the orifice is given as 0.1 m, so the radius will be 0.05 m. Therefore, the cross-sectional area of the orifice is A = π(0.05^2) = π(0.0025) = 0.00785 m^2.
Step 3: Convert the flow rate to volume flow rate
The flow rate is given as 20 liters/s. To convert this to a volume flow rate in cubic meters per second, we divide by 1000 (since 1 liter is equal to 0.001 cubic meters). Therefore, the volume flow rate is 20/1000 = 0.02 m^3/s.
Step 4: Apply the equation of continuity
The equation of continuity states that the volume flow rate of a fluid is constant at different cross-sectional areas. Therefore, we can equate the volume flow rate at the tank to the volume flow rate at the orifice:
A_tank * v_tank = A_orifice * v_orifice
Step 5: Calculate the velocity of water at the orifice
Rearranging the equation of continuity, we can solve for the velocity of water at the orifice:
v_orifice = (A_tank * v_tank) / A_orifice
Step 6: Apply the equation for velocity of efflux
The velocity of efflux can be calculated using the equation: v_efflux = √(2gh), where g is the acceleration due to gravity and h is the height of the water level in the tank.
Step 7: Apply the equation for the coefficient of discharge
The coefficient of discharge (Cd) relates the actual discharge to the theoretical discharge. It can be used to modify the equation for velocity of efflux:
v_efflux = Cd * √(2gh)
Step 8: Equate the equations for velocity of efflux and velocity at the orifice
Setting the equations for velocity of efflux and velocity at the orifice equal to each other, we can solve for the height of the water level (h):
Cd * √(2gh) = (A_tank * v_tank) / A_orifice
Step 9: Solve for the height of the water level
Rearranging the equation and plugging in the given values, we can solve for h:
h = [(Cd^2 * (A_tank^2 * v_tank^2)) / (2 * g * A_or
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A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer?
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A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer?.
A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular water tank of 2 m diameter has a circular orifice of diameter 0.1 m at the bottom.Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice.The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional loses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ______.Correct answer is '0.52'. Can you explain this answer?.
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