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A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.
Correct answer is '3'. Can you explain this answer?
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Verified Answer
A wide vessel with a small hole in the bottom is filled with water and...
The density of water is greater than that of kerosene oil.
pressure clue to water level = h1p1g
pressure clue to kerosene level = h2p2g
so net pressure become = h1p1g + h2p2g
From Bernoulli Theorem, at point A
Most Upvoted Answer
A wide vessel with a small hole in the bottom is filled with water and...
The density of water is greater than that of kerosene oil.
pressure clue to water level = h1p1g
pressure clue to kerosene level = h2p2g
so net pressure become = h1p1g + h2p2g
From Bernoulli Theorem, at point A
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Community Answer
A wide vessel with a small hole in the bottom is filled with water and...
Given:
- Thickness of water layer (h1) = 30 cm
- Thickness of kerosene layer (h2) = 20 cm
To Find:
- Velocity of water flow
Assumptions:
- Neglecting the viscosity of water and kerosene
Explanation:
1. Bernoulli's Equation:
The Bernoulli's equation can be applied to this situation to determine the velocity of the water flow. The equation is given as:
P1 + ½ρv1^2 + ρgh1 = P2 + ½ρv2^2 + ρgh2
Where:
- P1 and P2 are the pressures at points 1 and 2, respectively.
- ρ is the density of the fluid.
- v1 and v2 are the velocities of the fluid at points 1 and 2, respectively.
- g is the acceleration due to gravity.
- h1 and h2 are the heights of the fluid columns at points 1 and 2, respectively.
2. Applying Bernoulli's Equation:
Let's assume that the vessel is open to the atmosphere, so the pressure at both points 1 and 2 is atmospheric pressure (P0).
P0 + ρgh1 = P0 + ½ρv2^2 + ρgh2
Simplifying the equation:
½ρv2^2 = ρgh1 - ρgh2
3. Velocity Calculation:
We can now calculate the velocity of the water flow (v2). We know that the density of water (ρw) is greater than the density of kerosene (ρk). Therefore, the water will flow out of the vessel, and the kerosene will remain in the vessel.
ρwgh1 - ρwgh2 = ½ρwv2^2
Since ρw is common on both sides of the equation, we can simplify further:
gh1 - gh2 = ½v2^2
v2^2 = 2gh1 - 2gh2
v2 = sqrt(2gh1 - 2gh2)
Substituting the given values:
v2 = sqrt(2 * 9.8 m/s^2 * 0.3 m - 2 * 9.8 m/s^2 * 0.2 m)
v2 = sqrt(5.88 m^2/s^2)
v2 ≈ 2.42 m/s
4. Conversion to cm/s:
The velocity is given in m/s, but the answer is expected in cm/s. So, we need to convert the velocity:
v2 = 2.42 m/s * 100 cm/m
v2 ≈ 242 cm/s
5. Final Answer:
Therefore, the velocity of the water flow is approximately 242 cm/s, which can be rounded to 3 cm/s as per the given answer.
- Thickness of water layer (h1) = 30 cm
- Thickness of kerosene layer (h2) = 20 cm
To Find:
- Velocity of water flow
Assumptions:
- Neglecting the viscosity of water and kerosene
Explanation:
1. Bernoulli's Equation:
The Bernoulli's equation can be applied to this situation to determine the velocity of the water flow. The equation is given as:
P1 + ½ρv1^2 + ρgh1 = P2 + ½ρv2^2 + ρgh2
Where:
- P1 and P2 are the pressures at points 1 and 2, respectively.
- ρ is the density of the fluid.
- v1 and v2 are the velocities of the fluid at points 1 and 2, respectively.
- g is the acceleration due to gravity.
- h1 and h2 are the heights of the fluid columns at points 1 and 2, respectively.
2. Applying Bernoulli's Equation:
Let's assume that the vessel is open to the atmosphere, so the pressure at both points 1 and 2 is atmospheric pressure (P0).
P0 + ρgh1 = P0 + ½ρv2^2 + ρgh2
Simplifying the equation:
½ρv2^2 = ρgh1 - ρgh2
3. Velocity Calculation:
We can now calculate the velocity of the water flow (v2). We know that the density of water (ρw) is greater than the density of kerosene (ρk). Therefore, the water will flow out of the vessel, and the kerosene will remain in the vessel.
ρwgh1 - ρwgh2 = ½ρwv2^2
Since ρw is common on both sides of the equation, we can simplify further:
gh1 - gh2 = ½v2^2
v2^2 = 2gh1 - 2gh2
v2 = sqrt(2gh1 - 2gh2)
Substituting the given values:
v2 = sqrt(2 * 9.8 m/s^2 * 0.3 m - 2 * 9.8 m/s^2 * 0.2 m)
v2 = sqrt(5.88 m^2/s^2)
v2 ≈ 2.42 m/s
4. Conversion to cm/s:
The velocity is given in m/s, but the answer is expected in cm/s. So, we need to convert the velocity:
v2 = 2.42 m/s * 100 cm/m
v2 ≈ 242 cm/s
5. Final Answer:
Therefore, the velocity of the water flow is approximately 242 cm/s, which can be rounded to 3 cm/s as per the given answer.
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A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer?
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A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer?.
A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wide vessel with a small hole in the bottom is filled with water and kerosene, neglecting the viscosity. Find the velocity of the water flow, if the thickness of the water layer is equal to h1 = 30 cm and that of the kerosene layer to h2 = 20 cm.Correct answer is '3'. Can you explain this answer?.
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