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A rectangular tank is moving horizontally in the direction of its length with a constant acceleration of 4.5 m/s2.The length, width and depth of tank are 7 m, 3m, 2.5m respectively. If tank is open at the top then calculate the total force due to water acting on higher pressure end of the tank.
- a)1.07 MN
- b)2.14 MN
- c)4.28 MN
- d)4.35 MN
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A rectangular tank is moving horizontally in the direction of its leng...
Explanation: tanθ=a/g
tanθ=4.5/9.8
θ=24.64⁰
h= d+(L/2)tanθ
= 2.5+3.5tan24.64
= 4.1 m
tanθ=4.5/9.8
θ=24.64⁰
h= d+(L/2)tanθ
= 2.5+3.5tan24.64
= 4.1 m
F=wAĥ
=9810*2.68*4.1
= 1.07 MN.
=9810*2.68*4.1
= 1.07 MN.
Most Upvoted Answer
A rectangular tank is moving horizontally in the direction of its leng...
Given:
- Acceleration of the tank: 4.5 m/s^2
- Length of the tank: 7 m
- Width of the tank: 3 m
- Depth of the tank: 2.5 m
To find:
- Total force due to water acting on the higher pressure end of the tank
Assumptions:
- The tank is moving horizontally in the direction of its length.
- The tank is open at the top, which means the pressure at the top surface of the water is atmospheric pressure.
Approach:
- Determine the pressure difference between the higher and lower pressure ends of the tank.
- Calculate the force due to the pressure difference acting on the higher pressure end of the tank.
Solution:
Step 1: Determine the pressure difference between the higher and lower pressure ends of the tank.
The pressure at any point in a fluid is given by the equation:
P = P₀ + ρgh
Where:
- P is the pressure at the point
- P₀ is the reference pressure (atmospheric pressure)
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the depth of the point below the reference point
Since the tank is open at the top, the pressure at the top surface of the water is atmospheric pressure. So, the pressure at the higher pressure end of the tank is P₁ = P₀ + ρgh₁, where h₁ is the depth of the higher pressure end.
Similarly, the pressure at the lower pressure end of the tank is P₂ = P₀ + ρgh₂, where h₂ is the depth of the lower pressure end.
The pressure difference between the higher and lower pressure ends is given by:
ΔP = P₁ - P₂
ΔP = (P₀ + ρgh₁) - (P₀ + ρgh₂)
ΔP = ρg(h₁ - h₂)
Step 2: Calculate the force due to the pressure difference acting on the higher pressure end of the tank.
The force due to pressure is given by the equation:
F = A * ΔP
Where:
- F is the force
- A is the area
- ΔP is the pressure difference
The area of the higher pressure end of the tank is A = length * width.
Therefore, the force due to the pressure difference acting on the higher pressure end is:
F = (length * width) * ΔP
F = (7 m * 3 m) * ρg(h₁ - h₂)
Step 3: Substitute the given values and calculate the force.
The density of water, ρ = 1000 kg/m^3
The acceleration due to gravity, g = 9.8 m/s^2
The depth of the higher pressure end, h₁ = 2.5 m
The depth of the lower pressure end, h₂ = 0
F = (7 m * 3 m) * 1000 kg/m^3 * 9.8 m/s^2 * (2.5 m - 0)
F = 73500 N = 73.5 kN
Converting the force to mega newtons (MN):
- Acceleration of the tank: 4.5 m/s^2
- Length of the tank: 7 m
- Width of the tank: 3 m
- Depth of the tank: 2.5 m
To find:
- Total force due to water acting on the higher pressure end of the tank
Assumptions:
- The tank is moving horizontally in the direction of its length.
- The tank is open at the top, which means the pressure at the top surface of the water is atmospheric pressure.
Approach:
- Determine the pressure difference between the higher and lower pressure ends of the tank.
- Calculate the force due to the pressure difference acting on the higher pressure end of the tank.
Solution:
Step 1: Determine the pressure difference between the higher and lower pressure ends of the tank.
The pressure at any point in a fluid is given by the equation:
P = P₀ + ρgh
Where:
- P is the pressure at the point
- P₀ is the reference pressure (atmospheric pressure)
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the depth of the point below the reference point
Since the tank is open at the top, the pressure at the top surface of the water is atmospheric pressure. So, the pressure at the higher pressure end of the tank is P₁ = P₀ + ρgh₁, where h₁ is the depth of the higher pressure end.
Similarly, the pressure at the lower pressure end of the tank is P₂ = P₀ + ρgh₂, where h₂ is the depth of the lower pressure end.
The pressure difference between the higher and lower pressure ends is given by:
ΔP = P₁ - P₂
ΔP = (P₀ + ρgh₁) - (P₀ + ρgh₂)
ΔP = ρg(h₁ - h₂)
Step 2: Calculate the force due to the pressure difference acting on the higher pressure end of the tank.
The force due to pressure is given by the equation:
F = A * ΔP
Where:
- F is the force
- A is the area
- ΔP is the pressure difference
The area of the higher pressure end of the tank is A = length * width.
Therefore, the force due to the pressure difference acting on the higher pressure end is:
F = (length * width) * ΔP
F = (7 m * 3 m) * ρg(h₁ - h₂)
Step 3: Substitute the given values and calculate the force.
The density of water, ρ = 1000 kg/m^3
The acceleration due to gravity, g = 9.8 m/s^2
The depth of the higher pressure end, h₁ = 2.5 m
The depth of the lower pressure end, h₂ = 0
F = (7 m * 3 m) * 1000 kg/m^3 * 9.8 m/s^2 * (2.5 m - 0)
F = 73500 N = 73.5 kN
Converting the force to mega newtons (MN):
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A rectangular tank is moving horizontally in the direction of its length with a constant acceleration of 4.5 m/s2.The length, width and depth of tank are 7 m, 3m, 2.5m respectively. If tank is open at the top then calculate the total force due to water acting on higher pressure end of the tank.a)1.07 MNb)2.14 MNc)4.28 MNd)4.35 MNCorrect answer is option 'A'. Can you explain this answer?
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ample number of questions to practice A rectangular tank is moving horizontally in the direction of its length with a constant acceleration of 4.5 m/s2.The length, width and depth of tank are 7 m, 3m, 2.5m respectively. If tank is open at the top then calculate the total force due to water acting on higher pressure end of the tank.a)1.07 MNb)2.14 MNc)4.28 MNd)4.35 MNCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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