GATE ME 2018 Set 1 — Question 43
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Fluid Mechanics → Fluid Kinematics & Dynamics → Applications of Bernoulli
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Question
A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance (in m) where the jet strikes the floor is
Correct answer
(B) 1.0
Solution
Given:
Total water level m
Height of the hole from the floor mFirst, calculate the velocity of efflux () from the hole using Torricelli's Law. The height of water above the hole is m.
Assuming acceleration due to gravity (a common approximation in GATE if not specified).
Next, consider the projectile motion of the water jet. The jet leaves horizontally, so its initial vertical velocity is . The vertical distance it needs to fall to reach the floor is m.
The time () it takes for the jet to fall this vertical distance can be found using the equation of motion:
sFinally, calculate the horizontal distance () the jet travels during this time. Since the horizontal velocity is constant (), we have:
mThe distance where the jet strikes the floor is 1 m.The final answer is
Total water level m
Height of the hole from the floor mFirst, calculate the velocity of efflux () from the hole using Torricelli's Law. The height of water above the hole is m.
Assuming acceleration due to gravity (a common approximation in GATE if not specified).
Next, consider the projectile motion of the water jet. The jet leaves horizontally, so its initial vertical velocity is . The vertical distance it needs to fall to reach the floor is m.
The time () it takes for the jet to fall this vertical distance can be found using the equation of motion:
sFinally, calculate the horizontal distance () the jet travels during this time. Since the horizontal velocity is constant (), we have:
mThe distance where the jet strikes the floor is 1 m.The final answer is
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