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A conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.
Consider the following case.
Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.
(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).
Correct answer is 'Range: 260 to 265'. Can you explain this answer?
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Verified Answer
A conical flow passage converges uniformly from 0.2 m diameter to 0.1...
∴ U = Q(t) / A(x)
a = dU / dt
∴ a = ∂U / ∂t + U ∂U /∂x
a = 1 / A ∂Q / ∂t + Q 2 / A ∂/∂x (1 / A)
But A = πr2
Where a is the acceleration at section x (whose radius is r) at time instant t (when discharge is Q) Given that discharge increases from 100 Lt/sec to 200 Lt/sec in 5 seconds.
∴∂Q /∂t = (200 − 100) / 5 × 10−3 = 0.02 m3/sec2
Also Q(t = 2) = 0.1 + 0.02 × 2 = 0.14 m2/sec
As r = r1 + r2 − r1 / Lx
∴ r (x = L /2) = 0.1 +0.05 − 0.1 / 1 × 1 /2
r (x = L / 2) = 0.075 m
Also ∂r / ∂x =r2 − r1 / L = 0.05 − 0.1 / 1
∂r / ∂x = −0.05
= 1/π × (0.075)2 × 0.02 − 2 / π × (0.075)5 × 0.142 × (−0.05)
∴ a ( L / 2 , 2) = 264 m/sec2
Most Upvoted Answer
A conical flow passage converges uniformly from 0.2 m diameter to 0.1...
Problem Analysis:
To find the magnitude of total acceleration at the middle of the diffuser, we need to calculate the change in velocity and the time taken for the change. Given that the rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds, we can determine the initial and final velocities using the formula Q = A * V, where Q is the flow rate, A is the cross-sectional area, and V is the velocity.
Calculating Initial and Final Velocities:
Given:
- Initial flow rate (Q1) = 100 litres/s
- Final flow rate (Q2) = 200 litres/s
- Time taken (t) = 5 seconds
Step 1: Convert flow rates from litres/s to m^3/s
- Initial flow rate (Q1) = 100 litres/s = 0.1 m^3/s
- Final flow rate (Q2) = 200 litres/s = 0.2 m^3/s
Step 2: Determine the cross-sectional area at the initial and final flow rates
- Initial cross-sectional area (A1) = π * (0.1/2)^2 = 0.00785 m^2
- Final cross-sectional area (A2) = π * (0.2/2)^2 = 0.0314 m^2
Step 3: Calculate the initial and final velocities using the formula Q = A * V
- Initial velocity (V1) = Q1 / A1 = 0.1 / 0.00785 = 12.7 m/s
- Final velocity (V2) = Q2 / A2 = 0.2 / 0.0314 = 6.37 m/s
Calculating Change in Velocity:
To find the change in velocity, we subtract the initial velocity from the final velocity.
- Change in velocity (ΔV) = V2 - V1 = 6.37 - 12.7 = -6.33 m/s (negative sign indicates a decrease in velocity)
Calculating Time Taken:
The time of interest is t = 2 seconds.
Calculating Total Acceleration:
Using the formula for acceleration (a = ΔV / t), we can calculate the total acceleration at the middle of the diffuser.
- Total acceleration = ΔV / t = -6.33 / 2 = -3.17 m/s^2
However, the question asks for the magnitude of the total acceleration, which is always positive. Therefore, we take the absolute value of the total acceleration.
- Magnitude of total acceleration = |-3.17| = 3.17 m/s^2
Conclusion:
The magnitude of the total acceleration at the middle of the diffuser is 3.17 m/s^2.
To find the magnitude of total acceleration at the middle of the diffuser, we need to calculate the change in velocity and the time taken for the change. Given that the rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds, we can determine the initial and final velocities using the formula Q = A * V, where Q is the flow rate, A is the cross-sectional area, and V is the velocity.
Calculating Initial and Final Velocities:
Given:
- Initial flow rate (Q1) = 100 litres/s
- Final flow rate (Q2) = 200 litres/s
- Time taken (t) = 5 seconds
Step 1: Convert flow rates from litres/s to m^3/s
- Initial flow rate (Q1) = 100 litres/s = 0.1 m^3/s
- Final flow rate (Q2) = 200 litres/s = 0.2 m^3/s
Step 2: Determine the cross-sectional area at the initial and final flow rates
- Initial cross-sectional area (A1) = π * (0.1/2)^2 = 0.00785 m^2
- Final cross-sectional area (A2) = π * (0.2/2)^2 = 0.0314 m^2
Step 3: Calculate the initial and final velocities using the formula Q = A * V
- Initial velocity (V1) = Q1 / A1 = 0.1 / 0.00785 = 12.7 m/s
- Final velocity (V2) = Q2 / A2 = 0.2 / 0.0314 = 6.37 m/s
Calculating Change in Velocity:
To find the change in velocity, we subtract the initial velocity from the final velocity.
- Change in velocity (ΔV) = V2 - V1 = 6.37 - 12.7 = -6.33 m/s (negative sign indicates a decrease in velocity)
Calculating Time Taken:
The time of interest is t = 2 seconds.
Calculating Total Acceleration:
Using the formula for acceleration (a = ΔV / t), we can calculate the total acceleration at the middle of the diffuser.
- Total acceleration = ΔV / t = -6.33 / 2 = -3.17 m/s^2
However, the question asks for the magnitude of the total acceleration, which is always positive. Therefore, we take the absolute value of the total acceleration.
- Magnitude of total acceleration = |-3.17| = 3.17 m/s^2
Conclusion:
The magnitude of the total acceleration at the middle of the diffuser is 3.17 m/s^2.
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A conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. Can you explain this answer?
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A conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. 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 conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. 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 conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. Can you explain this answer?.
A conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. 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 conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. 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 conical flow passage converges uniformly from 0.2 m diameter to 0.1 m diameter over a length of 1 metre. Find the magnitude of total acceleration at the middle of the diffuser.Consider the following case.Rate of flow varies linearly from 100 litres/s to 200 litres/s in 5 seconds and the time of interest is t = 2 sec.(Velocity at any cross-section may be assumed to be uniform and perpendicular to the center line of passage).Correct answer is 'Range: 260 to 265'. Can you explain this answer?.
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