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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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 cm (d) 1.96 cm?
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A 50 cm diameter spherical vessel is completely filled up with a liqui...
Problem: Find the distance below the centre of the sphere where the points of maximum pressure lie when a 50 cm diameter spherical vessel, completely filled with a liquid of specific gravity 0.8, is rotated about the vertical axis at a rotational speed of 20 rad/s.
Solution:
Solution:
- Determine the angular velocity:
The angular velocity of the vessel can be determined using the formula:
ω = θ/t
where θ is the angle of rotation and t is the time taken for one rotation.
Since the vessel rotates at 20 rad/s, the time taken for one rotation is:
t = 2π/ω = 2π/20 = 0.314 s
Therefore, the angular velocity is:
ω = θ/t = 20 rad/s
- Determine the acceleration:
The acceleration of the liquid in the vessel can be determined using the formula:
a = rω2
where r is the radius of the vessel.
Since the diameter of the vessel is 50 cm, the radius is:
r = d/2 = 25 cm
Therefore, the acceleration is:
a = rω2 = (0.25 m) x (20 rad/s)2 = 100 m/s2
- Determine the pressure:
The pressure at any point in the liquid can be determined using the formula:
P = ρgh
where ρ is the density of the liquid, g is the acceleration due to gravity, and h is the depth of the point below the surface of the liquid.
Since the specific gravity of the liquid is 0.8, the density is:
ρ = 0.8 x 1000 kg/m3 = 800 kg/m3
Therefore, the pressure at any point can be expressed as:
P = 800 x 9.81 x h = 7848h Pa
- Determine the depth of the point of maximum pressure:
The point of maximum pressure lies on a horizontal plane below the centre of the sphere. Since the vessel is rotating about the
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A 50 cm diameter spherical vessel is completely filled up with a liqui...
1.96
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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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 cm (d) 1.96 cm? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 cm (d) 1.96 cm? covers all topics & solutions for Mechanical Engineering 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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 cm (d) 1.96 cm? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 cm (d) 1.96 cm? covers all topics & solutions for Mechanical Engineering 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 maximum pressure lie on a horizontal plane below the centre of sphere by (a) 12.5 cm (c) 2.45 cm (b) 6.96 cm (d) 1.96 cm?.
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