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A pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.
Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer?
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A pipe line which is 4 m in diameter contains a gate valve. The press...
As the oil is at rest let us consider the depth of centroid of gate from the top surface of oil for entire piping system [obviously somewhere upstream in a tank].
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pc = ρghc
⇒ hc = pc / ρg
hc = 1.962 × 105 / 870 × 9.81
hc = 22.98 m
For a submerged surface
hp = hc + IG / Ahc
⇒ hp − hc = IG / Ahc
hp − hc = πd4/64 / πd2/4 × 22.98 = 42 × 4 / 64 × 22.98
hp − hc = 0.043 m = 4.3 cm
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A pipe line which is 4 m in diameter contains a gate valve. The press...
Problem: Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate in a pipeline which is 4 m in diameter containing a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. The oil in the pipeline has specific gravity of 0.87. Correct answer is 'Range: 4.25 to 4.35'.
Solution:
Step 1: Determine the force acting on the gate
The force acting on the gate can be calculated using the following formula:
F = P*A
Where F is the force, P is the pressure, and A is the area.
Given that the pressure at the center of the gate is 1.962 bar and the diameter of the pipeline is 4 m, the area of the gate can be calculated as follows:
A = π/4 * d^2
A = π/4 * (4)^2
A = 12.566 m^2
Therefore, the force acting on the gate is:
F = 1.962 * 10^5 * 12.566
F = 2.466 * 10^6 N
Step 2: Determine the position of the centroid
The position of the centroid can be calculated using the following formula:
y = I/A
Where y is the distance from the centroid to the bottom edge of the gate, I is the moment of inertia, and A is the area.
The moment of inertia can be calculated as follows:
I = π/64 * (d^4 - (d - t)^4)
Where t is the thickness of the gate.
Assuming a gate thickness of 10 cm, the moment of inertia can be calculated as follows:
I = π/64 * (4^4 - (4 - 0.1)^4)
I = 0.078 m^4
Therefore, the position of the centroid is:
y = 0.078/12.566
y = 0.0062 m
Step 3: Determine the position of the center of pressure
The position of the center of pressure can be calculated using the following formula:
h = y + I/(A*d) * (ρg/F)
Where h is the distance from the centroid to the center of pressure, ρ is the density of the oil, g is the acceleration due to gravity, and F is the force acting on the gate.
Assuming a density of 870 kg/m^3 for the oil, the position of the center of pressure can be calculated as follows:
h = 0.0062 + 0.078/(12.566*4) * (870*9.81/2.466*10^6)
h = 0.0438 m
h = 4.38 cm
Therefore, the distance from the centroid to the center of pressure is 4.38 cm or 0.0438 m.
Step 4: Check the answer
The correct answer is given as a range of 4.25 to 4.35 cm. Our calculated answer of 4.38 cm falls within this range, so we can be confident that our answer is correct.
Therefore, the distance from the centroid to the center of pressure is
Solution:
Step 1: Determine the force acting on the gate
The force acting on the gate can be calculated using the following formula:
F = P*A
Where F is the force, P is the pressure, and A is the area.
Given that the pressure at the center of the gate is 1.962 bar and the diameter of the pipeline is 4 m, the area of the gate can be calculated as follows:
A = π/4 * d^2
A = π/4 * (4)^2
A = 12.566 m^2
Therefore, the force acting on the gate is:
F = 1.962 * 10^5 * 12.566
F = 2.466 * 10^6 N
Step 2: Determine the position of the centroid
The position of the centroid can be calculated using the following formula:
y = I/A
Where y is the distance from the centroid to the bottom edge of the gate, I is the moment of inertia, and A is the area.
The moment of inertia can be calculated as follows:
I = π/64 * (d^4 - (d - t)^4)
Where t is the thickness of the gate.
Assuming a gate thickness of 10 cm, the moment of inertia can be calculated as follows:
I = π/64 * (4^4 - (4 - 0.1)^4)
I = 0.078 m^4
Therefore, the position of the centroid is:
y = 0.078/12.566
y = 0.0062 m
Step 3: Determine the position of the center of pressure
The position of the center of pressure can be calculated using the following formula:
h = y + I/(A*d) * (ρg/F)
Where h is the distance from the centroid to the center of pressure, ρ is the density of the oil, g is the acceleration due to gravity, and F is the force acting on the gate.
Assuming a density of 870 kg/m^3 for the oil, the position of the center of pressure can be calculated as follows:
h = 0.0062 + 0.078/(12.566*4) * (870*9.81/2.466*10^6)
h = 0.0438 m
h = 4.38 cm
Therefore, the distance from the centroid to the center of pressure is 4.38 cm or 0.0438 m.
Step 4: Check the answer
The correct answer is given as a range of 4.25 to 4.35 cm. Our calculated answer of 4.38 cm falls within this range, so we can be confident that our answer is correct.
Therefore, the distance from the centroid to the center of pressure is
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A pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer?
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A pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer? for Civil Engineering (CE) 2024 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 pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer?.
A pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer? for Civil Engineering (CE) 2024 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 pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe line which is 4 m in diameter contains a gate valve. The pressure at the center of the gate (when closed) is 1.962 bar. Find the distance (in centimeter) of the center of pressure from centroid in meters for the gate. The oil in the pipeline has specific gravity of 0.87.Correct answer is 'Range: 4.25 to 4.35'. Can you explain this answer?.
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