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In a container, the velocity of water flowing through a hole at a depth h from the surface of water is 5 m-s⁻1. If the container has the hole at a depth 4h from the surface of water, then velocity of water flowing through the hole is
- a)5 m-s⁻1
- b)10 m-s⁻1
- c)20 m-s⁻1
- d)40 m-s⁻1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In a container, the velocity of water flowing through a hole at a dept...
Velocity of water flowing through a hole at a depth h from the surface of water is 5 m/s. We need to find the velocity of water flowing through the same hole if it is placed at a depth 4h from the surface of water.
Explanation:
Bernoulli's equation states that the sum of pressure, kinetic energy, and potential energy per unit volume of a fluid is constant at any point in the fluid.
Where P is the pressure of the fluid, ρ is the density of the fluid, g is the acceleration due to gravity, h is the height of the fluid above a reference point, and v is the velocity of the fluid.
We can apply Bernoulli's equation to find the velocity of water flowing through the hole at a depth 4h from the surface of water.
Since the hole is at the same level in both cases, the pressure at the hole is the same in both cases.
We can cancel out the constant term on both sides of the equation.
Rearranging the equation, we get:
Substituting the given values, we get:
Therefore, the velocity of water flowing through the hole at a depth 4h from the surface of water is 10 m/s, which is option (b).
Explanation:
Bernoulli's equation:
Bernoulli's equation states that the sum of pressure, kinetic energy, and potential energy per unit volume of a fluid is constant at any point in the fluid.
P + ρgh + ½ρv2 = constant
Where P is the pressure of the fluid, ρ is the density of the fluid, g is the acceleration due to gravity, h is the height of the fluid above a reference point, and v is the velocity of the fluid.
Application of Bernoulli's equation:
We can apply Bernoulli's equation to find the velocity of water flowing through the hole at a depth 4h from the surface of water.
At depth h: P1 + ρgh + ½ρv12 = constant
At depth 4h: P2 + ρg(4h) + ½ρv22 = constant
Since the hole is at the same level in both cases, the pressure at the hole is the same in both cases.
P1 = P2
We can cancel out the constant term on both sides of the equation.
ρgh + ½ρv12 = ρg(4h) + ½ρv22
Rearranging the equation, we get:
v2 = sqrt(v12 + 6gh)
Substituting the given values, we get:
v2 = sqrt(52 + 6*9.81*4h) = 10 m/s
Therefore, the velocity of water flowing through the hole at a depth 4h from the surface of water is 10 m/s, which is option (b).
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