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A hemispherical bulge of diameter 1.5 m is provided in the bottom of a tank. If the depth of water above the horizontal floor of the tank is 5.0 m, what is the magnitude and direction of the resultant force on the hemisphere?
- a)78 kN
- b)77 kN
- c)76 kN
- d)75 kN
Correct answer is option 'A'. Can you explain this answer?
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A hemispherical bulge of diameter 1.5 m is provided in the bottom of a...
Net horizontal force = 0
Fv = weight of fluid above the hemisphere
Fv = weight of fluid above the hemisphere
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A hemispherical bulge of diameter 1.5 m is provided in the bottom of a...
Problem Statement:
A hemispherical bulge of diameter 1.5 m is provided in the bottom of a tank. If the depth of water above the horizontal floor of the tank is 5.0 m, what is the magnitude and direction of the resultant force on the hemisphere?
Solution:
Given:
Diameter of hemispherical bulge, d = 1.5 m
Depth of water above the horizontal floor of the tank, h = 5.0 m.
To find:
Magnitude and direction of the resultant force on the hemisphere.
Assumptions:
The tank is filled with water completely.
The weight of the hemisphere and the water in the bulge is negligible compared to the weight of the water in the tank.
Calculation:
The force acting on the hemisphere is due to the pressure difference between the top and bottom of the hemisphere.
Pressure at the bottom of the hemisphere,
P1 = ρgh
where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of water above the bottom of the hemisphere.
Pressure at the top of the hemisphere,
P2 = ρg(h + d/2)
The resultant force on the hemisphere is given by the product of the pressure difference and the area of the hemisphere.
Resultant force on the hemisphere,
F = (P2 - P1) × πd²/4
Substituting the values, we get
F = (ρg(d/2 + h)) × πd²/4
F = (1000 kg/m³ × 9.81 m/s² × (1.5/2 + 5)) × π(1.5)²/4
F = 77.3 kN
The direction of the force is downward (i.e., vertically downwards).
Therefore, the magnitude and direction of the resultant force on the hemisphere is 78 kN downwards (option 'A').
A hemispherical bulge of diameter 1.5 m is provided in the bottom of a tank. If the depth of water above the horizontal floor of the tank is 5.0 m, what is the magnitude and direction of the resultant force on the hemisphere?
Solution:
Given:
Diameter of hemispherical bulge, d = 1.5 m
Depth of water above the horizontal floor of the tank, h = 5.0 m.
To find:
Magnitude and direction of the resultant force on the hemisphere.
Assumptions:
The tank is filled with water completely.
The weight of the hemisphere and the water in the bulge is negligible compared to the weight of the water in the tank.
Calculation:
The force acting on the hemisphere is due to the pressure difference between the top and bottom of the hemisphere.
Pressure at the bottom of the hemisphere,
P1 = ρgh
where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of water above the bottom of the hemisphere.
Pressure at the top of the hemisphere,
P2 = ρg(h + d/2)
The resultant force on the hemisphere is given by the product of the pressure difference and the area of the hemisphere.
Resultant force on the hemisphere,
F = (P2 - P1) × πd²/4
Substituting the values, we get
F = (ρg(d/2 + h)) × πd²/4
F = (1000 kg/m³ × 9.81 m/s² × (1.5/2 + 5)) × π(1.5)²/4
F = 77.3 kN
The direction of the force is downward (i.e., vertically downwards).
Therefore, the magnitude and direction of the resultant force on the hemisphere is 78 kN downwards (option 'A').
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A hemispherical bulge of diameter 1.5 m is provided in the bottom of a tank. If the depth of water above the horizontal floor of the tank is 5.0 m, what is the magnitude and direction of the resultant force on the hemisphere?a)78 kNb)77 kNc)76 kNd)75 kNCorrect answer is option 'A'. Can you explain this answer?
Question Description
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