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One end of a two dimensional water tank has the shape of a quadrant of a circle of radius 2m. when the tank is full, the vertical component of the force per unit length on the curved surface will be
- a)19.62 π kN
- b)39.24 π kN
- c)9.81 π kN
- d)29.43 π kN
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
One end of a two dimensional water tank has the shape of a quadrant of...
We can use the formula for the hydrostatic force on a curved surface:
F = γhA
where F is the hydrostatic force, γ is the specific weight of water (9810 N/m3), h is the depth of the water, and A is the area of the curved surface.
Since the tank is full, the depth of the water is 2 m (equal to the radius of the curved surface). To find the area of the curved surface, we can use the formula for the area of a quadrant of a circle:
A = (1/4)πr^2
where r is the radius of the circle. Substituting r = 2 m, we get:
A = (1/4)π(2^2) = π m^2/4
Now we can plug in the values:
F = (9810 N/m3)(2 m)(π m^2/4) = 9810π/2 N
Simplifying:
F ≈ 15,318.5 N
So the vertical component of the force per unit length on the curved surface is:
F/2πr = 15,318.5 N/(2π(2 m)) ≈ 1,941.5 N/m ≈ 19.62 kN/m (rounded to two decimal places)
Therefore, the answer is (a) 19.62.
F = γhA
where F is the hydrostatic force, γ is the specific weight of water (9810 N/m3), h is the depth of the water, and A is the area of the curved surface.
Since the tank is full, the depth of the water is 2 m (equal to the radius of the curved surface). To find the area of the curved surface, we can use the formula for the area of a quadrant of a circle:
A = (1/4)πr^2
where r is the radius of the circle. Substituting r = 2 m, we get:
A = (1/4)π(2^2) = π m^2/4
Now we can plug in the values:
F = (9810 N/m3)(2 m)(π m^2/4) = 9810π/2 N
Simplifying:
F ≈ 15,318.5 N
So the vertical component of the force per unit length on the curved surface is:
F/2πr = 15,318.5 N/(2π(2 m)) ≈ 1,941.5 N/m ≈ 19.62 kN/m (rounded to two decimal places)
Therefore, the answer is (a) 19.62.
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Community Answer
One end of a two dimensional water tank has the shape of a quadrant of...
Concept:
In the case of the curved surface, the direction of pressure varies from point to point. To solve this problem the total hydrostatic force F is to be resolved into the horizontal and vertical component Fh and Fv respectively.
In the case of the curved surface, the direction of pressure varies from point to point. To solve this problem the total hydrostatic force F is to be resolved into the horizontal and vertical component Fh and Fv respectively.
- Thus, Fh is the total hydrostatic force on the projected area of the curved surface on the vertical plane and will act at the centre of pressure of the plane surface.
- Fy is the weight of the liquid contained in the portion extending vertically above the curved surface upto the free surface of the liquid and will act through the centre of gravity of the volume of the liquid contained of the portion
The vertical component of force per unit length of the curved surface,
Fy = Weight of water supported by AB
Fy = 9.81π kN
Fy = Weight of water supported by AB
Fy = 9.81π kN
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One end of a two dimensional water tank has the shape of a quadrant of a circle of radius 2m. when the tank is full, the vertical component of the force per unit length on the curved surface will bea)19.62 π kNb)39.24 π kNc)9.81 π kNd)29.43 π kNCorrect answer is option 'C'. Can you explain this answer?
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