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When a cylindrical vessel containing liquid is revolved about its vertical axis at a constant angular velocity, the pressure
- a)varies linearly as its radial distance
- b)varies as the square of the radial distance
- c)varies as the cube of the radial distance
- d)remains constant
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
When a cylindrical vessel containing liquid is revolved about its vert...
Variation in pressure in horizontal direction in a rotating cylindrical vessel containing fluid is given by,
∂P/∂r = pw2r
∂P/∂r = pw2r
Most Upvoted Answer
When a cylindrical vessel containing liquid is revolved about its vert...
**Explanation:**
When a cylindrical vessel containing liquid is revolved about its vertical axis at a constant angular velocity, the pressure distribution within the liquid will vary.
**Pressure Distribution:**
The pressure distribution within the liquid can be determined using the concept of centrifugal force. As the liquid is being rotated, each element of the liquid experiences a centrifugal force directed outward from the axis of rotation. This centrifugal force is balanced by the pressure gradient in the liquid.
**Pressure Variation:**
The pressure variation within the liquid can be determined by considering a small element of liquid located at a radial distance 'r' from the axis of rotation.
1. **Horizontal Forces:** The horizontal forces acting on the element are the centrifugal force (directed outward) and the pressure force (directed inward). These forces should balance each other for the element to be in equilibrium.
2. **Centrifugal Force:** The centrifugal force acting on the element is given by Fc = mω²r, where m is the mass of the element and ω is the angular velocity.
3. **Pressure Force:** The pressure force acting on the element is given by Fp = ∆P × A, where ∆P is the pressure difference across the element and A is the area of the element.
4. **Equilibrium Condition:** For the element to be in equilibrium, the centrifugal force and the pressure force should be equal. Therefore, Fc = Fp.
5. **Pressure Variation:** From the above equations, we can write ∆P × A = mω²r. As the mass of the element (m) and the angular velocity (ω) remain constant, the pressure difference (∆P) will vary linearly with the radial distance (r).
**Conclusion:**
Therefore, the pressure within the liquid varies linearly with the radial distance from the axis of rotation. Hence, the correct answer is option 'A' - varies linearly as its radial distance.
When a cylindrical vessel containing liquid is revolved about its vertical axis at a constant angular velocity, the pressure distribution within the liquid will vary.
**Pressure Distribution:**
The pressure distribution within the liquid can be determined using the concept of centrifugal force. As the liquid is being rotated, each element of the liquid experiences a centrifugal force directed outward from the axis of rotation. This centrifugal force is balanced by the pressure gradient in the liquid.
**Pressure Variation:**
The pressure variation within the liquid can be determined by considering a small element of liquid located at a radial distance 'r' from the axis of rotation.
1. **Horizontal Forces:** The horizontal forces acting on the element are the centrifugal force (directed outward) and the pressure force (directed inward). These forces should balance each other for the element to be in equilibrium.
2. **Centrifugal Force:** The centrifugal force acting on the element is given by Fc = mω²r, where m is the mass of the element and ω is the angular velocity.
3. **Pressure Force:** The pressure force acting on the element is given by Fp = ∆P × A, where ∆P is the pressure difference across the element and A is the area of the element.
4. **Equilibrium Condition:** For the element to be in equilibrium, the centrifugal force and the pressure force should be equal. Therefore, Fc = Fp.
5. **Pressure Variation:** From the above equations, we can write ∆P × A = mω²r. As the mass of the element (m) and the angular velocity (ω) remain constant, the pressure difference (∆P) will vary linearly with the radial distance (r).
**Conclusion:**
Therefore, the pressure within the liquid varies linearly with the radial distance from the axis of rotation. Hence, the correct answer is option 'A' - varies linearly as its radial distance.
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When a cylindrical vessel containing liquid is revolved about its vertical axis at a constant angular velocity, the pressurea)varies linearly as its radial distanceb)varies as the square of the radial distancec)varies as the cube of the radial distanced)remains constantCorrect answer is option 'A'. Can you explain this answer?
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