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Water (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2 is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.
Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1
is _________
Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1
is _________
Important : you should answer only the numeric value
Correct answer is '137500'. Can you explain this answer?
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Water (density 1000 kg/m3) is flowing through a nozzle, as shown below...
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Water (density 1000 kg/m3) is flowing through a nozzle, as shown below...
Given:
- Density of water (ρ) = 1000 kg/m3
- Diameter at location 1 (D1) = 4D2
- Velocity at location 2 (V2) = 16 m/s
- Frictional loss between location 1 and 2 (ΔP) = 10000 Pa
To find:
- Gauge pressure at location 1 (P1)
Formula:
The Bernoulli's equation can be used to solve this problem. The Bernoulli's equation states that the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline in a steady flow.
P1 + 0.5ρV1^2 + ρgh1 = P2 + 0.5ρV2^2 + ρgh2
In this case, the potential energy h1 and h2 can be assumed to be the same since the stream is exiting to the atmosphere. Therefore, the equation simplifies to:
P1 + 0.5ρV1^2 = P2 + 0.5ρV2^2
Calculation:
Given:
D1 = 4D2
We know that the velocity of a fluid flowing through a nozzle is inversely proportional to the cross-sectional area. Therefore, we can write the equation:
A1V1 = A2V2
Substituting the values:
(π/4)D1^2 * V1 = (π/4)D2^2 * V2
(π/4)(4D2)^2 * V1 = (π/4)D2^2 * 16
16D2^2 * V1 = D2^2 * 16
D2^2 cancels out, and we are left with:
D2^2 * V1 = V2
V1 = V2/D2^2
Substituting this value in the Bernoulli's equation:
P1 + 0.5ρ(V2/D2^2)^2 = P2 + 0.5ρV2^2
P1 + 0.5ρV2^2/D2^4 = P2 + 0.5ρV2^2
P1 - P2 = 0.5ρV2^2(1 - 1/D2^4)
P1 = P2 + 0.5ρV2^2(1 - 1/D2^4)
Given:
P2 = atmospheric pressure = 0 (since stream is exiting to the atmosphere)
P1 = 0 + 0.5 * 1000 * 16^2 * (1 - 1/(4^4))
P1 = 0 + 0.5 * 1000 * 256 * (1 - 1/256)
P1 = 0 + 0.5 * 1000 * 256 * (255/256)
P1 = 0.5 * 1000 * 256 * 255
P1 = 137500
Therefore, the gauge pressure at location 1 is 137500 Pa.
- Density of water (ρ) = 1000 kg/m3
- Diameter at location 1 (D1) = 4D2
- Velocity at location 2 (V2) = 16 m/s
- Frictional loss between location 1 and 2 (ΔP) = 10000 Pa
To find:
- Gauge pressure at location 1 (P1)
Formula:
The Bernoulli's equation can be used to solve this problem. The Bernoulli's equation states that the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline in a steady flow.
P1 + 0.5ρV1^2 + ρgh1 = P2 + 0.5ρV2^2 + ρgh2
In this case, the potential energy h1 and h2 can be assumed to be the same since the stream is exiting to the atmosphere. Therefore, the equation simplifies to:
P1 + 0.5ρV1^2 = P2 + 0.5ρV2^2
Calculation:
Given:
D1 = 4D2
We know that the velocity of a fluid flowing through a nozzle is inversely proportional to the cross-sectional area. Therefore, we can write the equation:
A1V1 = A2V2
Substituting the values:
(π/4)D1^2 * V1 = (π/4)D2^2 * V2
(π/4)(4D2)^2 * V1 = (π/4)D2^2 * 16
16D2^2 * V1 = D2^2 * 16
D2^2 cancels out, and we are left with:
D2^2 * V1 = V2
V1 = V2/D2^2
Substituting this value in the Bernoulli's equation:
P1 + 0.5ρ(V2/D2^2)^2 = P2 + 0.5ρV2^2
P1 + 0.5ρV2^2/D2^4 = P2 + 0.5ρV2^2
P1 - P2 = 0.5ρV2^2(1 - 1/D2^4)
P1 = P2 + 0.5ρV2^2(1 - 1/D2^4)
Given:
P2 = atmospheric pressure = 0 (since stream is exiting to the atmosphere)
P1 = 0 + 0.5 * 1000 * 16^2 * (1 - 1/(4^4))
P1 = 0 + 0.5 * 1000 * 256 * (1 - 1/256)
P1 = 0 + 0.5 * 1000 * 256 * (255/256)
P1 = 0.5 * 1000 * 256 * 255
P1 = 137500
Therefore, the gauge pressure at location 1 is 137500 Pa.
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Water (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. Can you explain this answer?
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Water (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. 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 (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. 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 (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. Can you explain this answer?.
Water (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. 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 (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. 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 (density 1000 kg/m3) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D1 = 4 D2. The average velocity of the stream at location 2is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1is _________Important : you should answer only the numeric valueCorrect answer is '137500'. Can you explain this answer?.
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