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A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:
- a)4
- b)2
- c)1
- d)0.5
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A house-top water tank is made of flat plates and is full to the brim....
Understanding the Water Tank Configuration
The house-top water tank is a cuboidal shape where the height (H) is twice the length (L) and width (B). Therefore, we can express the dimensions as:
- Height (H) = 2L
- Width (B) = L
This gives the tank a height of twice the size of any side.
Calculating the Total Thrust Force
The thrust force on any surface of the tank is related to the hydrostatic pressure exerted by the water.
- **Hydrostatic Pressure (P)** at a depth (h) is given by:
P = ρgh
where ρ is the density of water, g is the acceleration due to gravity, and h is the depth.
- **Total Thrust Force (F)** on a surface can be calculated as:
F = P × Area
where Area is the area of the surface.
Thrust Force on the Bottom of the Tank
For the bottom of the tank:
- Depth (h) = H = 2L
- Area of the bottom = L × L = L²
Thus, the total thrust force on the bottom is:
F_bottom = ρg(2L) × L² = 2ρgL³
Thrust Force on the Sides of the Tank
For one side of the tank:
- Depth (h) varies from 0 to H = 2L. The average depth is L.
- Area of one side = H × B = (2L) × L = 2L²
Thus, the total thrust force on one side is:
F_side = ρg(L) × 2L² = 2ρgL³
Ratio of Total Thrust Forces
The ratio of the total thrust force on the bottom to that on one side is:
Ratio = F_bottom / F_side = (2ρgL³) / (2ρgL³) = 1
Therefore, the ratio of the total thrust force on the bottom of the tank to that on any side is **1**, which confirms that the correct answer is option 'C'.
The house-top water tank is a cuboidal shape where the height (H) is twice the length (L) and width (B). Therefore, we can express the dimensions as:
- Height (H) = 2L
- Width (B) = L
This gives the tank a height of twice the size of any side.
Calculating the Total Thrust Force
The thrust force on any surface of the tank is related to the hydrostatic pressure exerted by the water.
- **Hydrostatic Pressure (P)** at a depth (h) is given by:
P = ρgh
where ρ is the density of water, g is the acceleration due to gravity, and h is the depth.
- **Total Thrust Force (F)** on a surface can be calculated as:
F = P × Area
where Area is the area of the surface.
Thrust Force on the Bottom of the Tank
For the bottom of the tank:
- Depth (h) = H = 2L
- Area of the bottom = L × L = L²
Thus, the total thrust force on the bottom is:
F_bottom = ρg(2L) × L² = 2ρgL³
Thrust Force on the Sides of the Tank
For one side of the tank:
- Depth (h) varies from 0 to H = 2L. The average depth is L.
- Area of one side = H × B = (2L) × L = 2L²
Thus, the total thrust force on one side is:
F_side = ρg(L) × 2L² = 2ρgL³
Ratio of Total Thrust Forces
The ratio of the total thrust force on the bottom to that on one side is:
Ratio = F_bottom / F_side = (2ρgL³) / (2ρgL³) = 1
Therefore, the ratio of the total thrust force on the bottom of the tank to that on any side is **1**, which confirms that the correct answer is option 'C'.
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Community Answer
A house-top water tank is made of flat plates and is full to the brim....
Concept:
Whenever a static mass of fluid comes into contact with a surface the fluid exerts force upon that surface. The magnitude of this force is known as the hydrostatic force or total pressure force.
The magnitude of hydrostatic force is given by F = ρ g h̅̅ A N
Where ρ = Density of the fluid, h̅ = Depth of center of gravity of the surface from free liquid surface, A = Area of the surface
Calcualtion:
Given tank has the height twice as the width of the tank.
Pressure force acting on the vertical surface:
The center of gravity of the vertical surface from the free surface will be
h¯= 2x/2 = xm
Area of the vertical surface = 2x × x = 2x2
Now the Pressure force ρ × g × x × 2x2 = 2ρgx3
Now, the force on the bottom surface:
The center of gravity of the bottom surface from the free liquid surface = hieht of the tank = 2x
Area of the bottom surface = x × x = x2
Now the pressure force = ρ × g × 2x × x2 = 2ρgx3
Therefore the ratio of the forces will be one as the forces on the bottom side and the vertical sides are equal.
Whenever a static mass of fluid comes into contact with a surface the fluid exerts force upon that surface. The magnitude of this force is known as the hydrostatic force or total pressure force.
The magnitude of hydrostatic force is given by F = ρ g h̅̅ A N
Where ρ = Density of the fluid, h̅ = Depth of center of gravity of the surface from free liquid surface, A = Area of the surface
Calcualtion:
Given tank has the height twice as the width of the tank.
Pressure force acting on the vertical surface:
The center of gravity of the vertical surface from the free surface will be
h¯= 2x/2 = xm
Area of the vertical surface = 2x × x = 2x2
Now the Pressure force ρ × g × x × 2x2 = 2ρgx3
Now, the force on the bottom surface:
The center of gravity of the bottom surface from the free liquid surface = hieht of the tank = 2x
Area of the bottom surface = x × x = x2
Now the pressure force = ρ × g × 2x × x2 = 2ρgx3
Therefore the ratio of the forces will be one as the forces on the bottom side and the vertical sides are equal.
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A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:a)4b)2c)1d)0.5Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:a)4b)2c)1d)0.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:a)4b)2c)1d)0.5Correct answer is option 'C'. Can you explain this answer?.
A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:a)4b)2c)1d)0.5Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:a)4b)2c)1d)0.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:a)4b)2c)1d)0.5Correct answer is option 'C'. Can you explain this answer?.
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