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Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcy's friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s. Assume gravitational acceleration, g = 10 m/s2. The value of h is _______m
Correct answer is between '9.7,10.3'. Can you explain this answer?
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Water is discharged at atmospheric pressure from a large reservoir thr...
M3/s.
To find:
a) The pressure at the discharge point.
b) The velocity of water at the discharge point.
c) The head loss in the pipe.
Solution:
a) The pressure at the discharge point can be found using Bernoulli's equation, which states that the sum of pressure, kinetic energy and potential energy per unit volume is constant along a streamline.
P1/ρ + v1^2/2g + h1 = P2/ρ + v2^2/2g + h2
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, g is the acceleration due to gravity, and h1 and h2 are the heights of points 1 and 2 respectively above a reference plane.
At point 1, the velocity is zero and the pressure is atmospheric (since the water is discharged into the atmosphere). The height of point 1 above the reference plane is h. At point 2, the velocity is v2 and the height of point 2 above the reference plane is zero.
Therefore, P2/ρ = h + v2^2/2g
P2 = ρgh + ρv2^2/2
Substituting the given values, we get:
P2 = 1000 x 9.81 x 20 + 1000 x (4/π x (0.04/2)^2)^2/2
P2 = 198200 Pa
Therefore, the pressure at the discharge point is 198200 Pa.
b) The velocity of water at the discharge point can be found using the continuity equation, which states that the mass flow rate is constant along a streamline.
ρAv = Q
where ρ is the density of water, A is the cross-sectional area of the pipe, v is the velocity of water and Q is the flow rate.
Substituting the given values, we get:
v = Q/(ρA)
A = πd^2/4 = π(0.04)^2/4 = 0.001256 m^2
v = 4/(1000 x 0.001256) = 3.18 m/s
Therefore, the velocity of water at the discharge point is 3.18 m/s.
c) The head loss in the pipe can be found using the Darcy-Weisbach equation, which relates the head loss (hL) to the friction factor (f), length of the pipe (L), diameter of the pipe (d), velocity of water (v) and acceleration due to gravity (g).
hL = fL(v^2/2gd)
Substituting the given values, we get:
hL = 0.002 x 20 x (3.18^2/2 x 9.81 x 0.04/2) = 0.98 m
Therefore, the head loss in the pipe is 0.98 m.
To find:
a) The pressure at the discharge point.
b) The velocity of water at the discharge point.
c) The head loss in the pipe.
Solution:
a) The pressure at the discharge point can be found using Bernoulli's equation, which states that the sum of pressure, kinetic energy and potential energy per unit volume is constant along a streamline.
P1/ρ + v1^2/2g + h1 = P2/ρ + v2^2/2g + h2
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, g is the acceleration due to gravity, and h1 and h2 are the heights of points 1 and 2 respectively above a reference plane.
At point 1, the velocity is zero and the pressure is atmospheric (since the water is discharged into the atmosphere). The height of point 1 above the reference plane is h. At point 2, the velocity is v2 and the height of point 2 above the reference plane is zero.
Therefore, P2/ρ = h + v2^2/2g
P2 = ρgh + ρv2^2/2
Substituting the given values, we get:
P2 = 1000 x 9.81 x 20 + 1000 x (4/π x (0.04/2)^2)^2/2
P2 = 198200 Pa
Therefore, the pressure at the discharge point is 198200 Pa.
b) The velocity of water at the discharge point can be found using the continuity equation, which states that the mass flow rate is constant along a streamline.
ρAv = Q
where ρ is the density of water, A is the cross-sectional area of the pipe, v is the velocity of water and Q is the flow rate.
Substituting the given values, we get:
v = Q/(ρA)
A = πd^2/4 = π(0.04)^2/4 = 0.001256 m^2
v = 4/(1000 x 0.001256) = 3.18 m/s
Therefore, the velocity of water at the discharge point is 3.18 m/s.
c) The head loss in the pipe can be found using the Darcy-Weisbach equation, which relates the head loss (hL) to the friction factor (f), length of the pipe (L), diameter of the pipe (d), velocity of water (v) and acceleration due to gravity (g).
hL = fL(v^2/2gd)
Substituting the given values, we get:
hL = 0.002 x 20 x (3.18^2/2 x 9.81 x 0.04/2) = 0.98 m
Therefore, the head loss in the pipe is 0.98 m.
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Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. Can you explain this answer?
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Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. 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 Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. Can you explain this answer?.
Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. 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 Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. Can you explain this answer?.
Solutions for Water is discharged at atmospheric pressure from a large reservoir through a long pipe of diameter d and length L. The height of the free surface of the reservoir from the discharge point is h meters. The Darcys friction factor of the pipe is 0.002. Neglect the velocity inside the reservoir as the reservoir is very large. Given, L = 20m, d = 40mm, density of water = 1000kg/m3 and flow rate is Q=4π x 10-3m3/s.Assume gravitational acceleration, g = 10 m/s2. The value of h is _______mCorrect answer is between '9.7,10.3'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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