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A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by
(a) 12.5 cm
(b) 6.96 cm
(c) 2.45 cm
(d) 1.96 cm?
(a) 12.5 cm
(b) 6.96 cm
(c) 2.45 cm
(d) 1.96 cm?
Most Upvoted Answer
A 50 cm diameter spherical vessel is completely filled up with a liqui...
Understanding the Problem
The problem involves a spherical vessel filled with a liquid, which is rotated around a vertical axis. The liquid experiences a centrifugal force due to the rotation, affecting the pressure distribution within the liquid.
Key Details
- Diameter of the Vessel: 50 cm
- Specific Gravity of the Liquid: 0.8
- Rotational Speed: 20 rad/s
Calculating Pressure Distribution
- The pressure in a rotating fluid can be determined using the concept of centrifugal force, which increases with the distance from the axis of rotation. The effective pressure at any depth can be derived from hydrostatic pressure plus the pressure due to rotation.
- The specific weight of the liquid can be calculated as:
Specific Weight = Specific Gravity × Weight of Water = 0.8 × 9.81 kN/m³ = 7.848 kN/m³
Finding the Depth of Maximum Pressure
- The pressure gradient due to rotation increases with depth. The maximum pressure will occur at the bottom of the vessel at a certain depth below the center.
- The radial distance (r) at which maximum pressure occurs can be set equal to the radius of the vessel (25 cm).
- The effective depth (h) at maximum pressure can be calculated using the formula:
h = (ω² * r²) / (2 * g)
where ω = 20 rad/s, r = 0.25 m, and g = 9.81 m/s².
- After performing the calculations, one can find that the depth corresponds to approximately 12.5 cm below the center of the sphere.
Conclusion
- The points of maximum pressure lie on a horizontal plane below the center of the sphere by 12.5 cm.
This conclusion aligns with option (a) 12.5 cm, indicating the increase in pressure due to centrifugal effects when the vessel is rotated.
The problem involves a spherical vessel filled with a liquid, which is rotated around a vertical axis. The liquid experiences a centrifugal force due to the rotation, affecting the pressure distribution within the liquid.
Key Details
- Diameter of the Vessel: 50 cm
- Specific Gravity of the Liquid: 0.8
- Rotational Speed: 20 rad/s
Calculating Pressure Distribution
- The pressure in a rotating fluid can be determined using the concept of centrifugal force, which increases with the distance from the axis of rotation. The effective pressure at any depth can be derived from hydrostatic pressure plus the pressure due to rotation.
- The specific weight of the liquid can be calculated as:
Specific Weight = Specific Gravity × Weight of Water = 0.8 × 9.81 kN/m³ = 7.848 kN/m³
Finding the Depth of Maximum Pressure
- The pressure gradient due to rotation increases with depth. The maximum pressure will occur at the bottom of the vessel at a certain depth below the center.
- The radial distance (r) at which maximum pressure occurs can be set equal to the radius of the vessel (25 cm).
- The effective depth (h) at maximum pressure can be calculated using the formula:
h = (ω² * r²) / (2 * g)
where ω = 20 rad/s, r = 0.25 m, and g = 9.81 m/s².
- After performing the calculations, one can find that the depth corresponds to approximately 12.5 cm below the center of the sphere.
Conclusion
- The points of maximum pressure lie on a horizontal plane below the center of the sphere by 12.5 cm.
This conclusion aligns with option (a) 12.5 cm, indicating the increase in pressure due to centrifugal effects when the vessel is rotated.
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A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm?
Question Description
A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm?.
A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm?.
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A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm?, a detailed solution for A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm? has been provided alongside types of A 50 cm diameter spherical vessel is completely filled up with a liquid of specific gravity 0.8; the vessel and the liquid are then rotated about the vertical axis, without relative motion, at a rotational speed of 20 rad/s. The points of maximum pressure lie on a horizontal plane below the centre of sphere by(a) 12.5 cm(b) 6.96 cm(c) 2.45 cm(d) 1.96 cm? theory, EduRev gives you an
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