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A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.
Correct answer is '2.56'. Can you explain this answer?
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A cast iron pipe of diameter 600 mm and length 400 m carries water fro...
Apply energy equation between (1) and (2)
V2 = 6.54
V = 2.557 m/s ≌ 2.56 m/s
Most Upvoted Answer
A cast iron pipe of diameter 600 mm and length 400 m carries water fro...
Given data:
Diameter of the pipe (D) = 600 mm = 0.6 m
Length of the pipe (L) = 400 m
Height difference between the water surface and the discharge point (H) = 4.5 m
Friction factor of the pipe (f) = 0.018
Acceleration due to gravity (g) = 9.81 m/s²
Calculating the velocity of the flow:
The velocity of the flow in the pipe can be calculated using the Bernoulli's equation, which states that the total head at any two points of a fluid flow system remains constant.
Total head at point 1 (water surface in the tank):
P₁/ρg + V₁²/2g + Z₁ = Constant
Total head at point 2 (discharge point):
P₂/ρg + V₂²/2g + Z₂ = Constant
Where:
P₁ and P₂ are the pressures at points 1 and 2 respectively,
ρ is the density of water,
V₁ and V₂ are the velocities at points 1 and 2 respectively,
Z₁ and Z₂ are the heights at points 1 and 2 respectively.
Since the water discharges freely into the air, the pressure at point 2 can be assumed to be atmospheric pressure (P₂ = 0).
At point 1:
P₁/ρg + V₁²/2g + Z₁ = P₂/ρg + V₂²/2g + Z₂
P₁/ρg + V₁²/2g + 0 = 0/ρg + V₂²/2g + H
Simplifying the equation and rearranging:
V₁²/2g - V₂²/2g = H
(V₁² - V₂²)/2g = H
V₁² - V₂² = 2gH
V₁² = 2gH + V₂²
The friction factor (f) can be used to calculate the head loss due to friction using the Darcy-Weisbach equation:
hf = f(L/D) * (V²/2g)
Substituting the values and solving for V²:
hf = f(L/D) * (V²/2g)
V² = 2g(hf) / (f(L/D))
Since the pipe discharges freely into the air, the head loss due to friction (hf) is equal to the height difference between the water surface and the discharge point (H).
Substituting the values and solving for V²:
V² = 2g(H) / (f(L/D))
V² = 2 * 9.81 * 4.5 / (0.018 * (400/0.6))
V² = 2 * 9.81 * 4.5 / (0.018 * 666.67)
V² = 2 * 44.145 / 12
V² = 88.29 / 12
V² ≈ 7.36
Taking the square root of both sides:
V ≈ √7.36
V ≈ 2.71
Rounding off to two decimal places, the velocity of the flow in the pipe is approximately 2.71 m/s
Diameter of the pipe (D) = 600 mm = 0.6 m
Length of the pipe (L) = 400 m
Height difference between the water surface and the discharge point (H) = 4.5 m
Friction factor of the pipe (f) = 0.018
Acceleration due to gravity (g) = 9.81 m/s²
Calculating the velocity of the flow:
The velocity of the flow in the pipe can be calculated using the Bernoulli's equation, which states that the total head at any two points of a fluid flow system remains constant.
Total head at point 1 (water surface in the tank):
P₁/ρg + V₁²/2g + Z₁ = Constant
Total head at point 2 (discharge point):
P₂/ρg + V₂²/2g + Z₂ = Constant
Where:
P₁ and P₂ are the pressures at points 1 and 2 respectively,
ρ is the density of water,
V₁ and V₂ are the velocities at points 1 and 2 respectively,
Z₁ and Z₂ are the heights at points 1 and 2 respectively.
Since the water discharges freely into the air, the pressure at point 2 can be assumed to be atmospheric pressure (P₂ = 0).
At point 1:
P₁/ρg + V₁²/2g + Z₁ = P₂/ρg + V₂²/2g + Z₂
P₁/ρg + V₁²/2g + 0 = 0/ρg + V₂²/2g + H
Simplifying the equation and rearranging:
V₁²/2g - V₂²/2g = H
(V₁² - V₂²)/2g = H
V₁² - V₂² = 2gH
V₁² = 2gH + V₂²
The friction factor (f) can be used to calculate the head loss due to friction using the Darcy-Weisbach equation:
hf = f(L/D) * (V²/2g)
Substituting the values and solving for V²:
hf = f(L/D) * (V²/2g)
V² = 2g(hf) / (f(L/D))
Since the pipe discharges freely into the air, the head loss due to friction (hf) is equal to the height difference between the water surface and the discharge point (H).
Substituting the values and solving for V²:
V² = 2g(H) / (f(L/D))
V² = 2 * 9.81 * 4.5 / (0.018 * (400/0.6))
V² = 2 * 9.81 * 4.5 / (0.018 * 666.67)
V² = 2 * 44.145 / 12
V² = 88.29 / 12
V² ≈ 7.36
Taking the square root of both sides:
V ≈ √7.36
V ≈ 2.71
Rounding off to two decimal places, the velocity of the flow in the pipe is approximately 2.71 m/s
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A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer?
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A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer?.
A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is __________.Correct answer is '2.56'. Can you explain this answer?.
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