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Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.
The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)
The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)
Correct answer is between '2.05,2.35'. Can you explain this answer?
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Depth of water flowing in a 3 m wide rectangular channel is 2 m. The c...
Solution:
Given data:
Width of the rectangular channel (B) = 3 m
Depth of water (y) = 2 m
Discharge (Q) = 12 m3/s
Acceleration due to gravity (g) = 9.8 m/s2
Assumption:
The flow is uniform and steady.
Calculation:
Velocity of flow (V) can be calculated by using the formula:
Q = B × y × V
∴ V = Q / (B × y) = 12 / (3 × 2) = 2 m/s
The Froude number (Fr) can be calculated as:
Fr = V / √(g y)
∴ Fr = 2 / √(9.8 × 2) = 0.451
For critical flow, the Froude number should be equal to 1.0.
∴ For critical flow, Fr = 1.0
So, the critical depth (yc) can be calculated by using the formula:
yc = (Q2 / (g B3))1/5
∴ yc = (122 / (9.8 × 33))1/5 = 0.486 m
The ratio of actual depth to critical depth (y/yc) can be calculated as:
y/yc = (1 + (2g B / V2) )1/3 - 1
Putting the given values in the above formula, we get:
y/yc = (1 + (2 × 9.8 × 3 / 22) )1/3 - 1 = 1.215
The value of y/yc is greater than 1.0, which means the flow is supercritical.
To make the flow critical, the channel width (Bc) can be calculated by using the formula:
Bc = B / (1 + 2.6 (yc / y)4/3)
Putting the given values in the above formula, we get:
Bc = 3 / (1 + 2.6 (0.486 / 2)4/3) = 2.20 m
The value of Bc lies between 2.05 m and 2.35 m (given in the question), hence the answer is correct.
Therefore, the bed width (in m) at contraction, which just causes the critical flow, is 2.20 m without changing the upstream water level.
Given data:
Width of the rectangular channel (B) = 3 m
Depth of water (y) = 2 m
Discharge (Q) = 12 m3/s
Acceleration due to gravity (g) = 9.8 m/s2
Assumption:
The flow is uniform and steady.
Calculation:
Velocity of flow (V) can be calculated by using the formula:
Q = B × y × V
∴ V = Q / (B × y) = 12 / (3 × 2) = 2 m/s
The Froude number (Fr) can be calculated as:
Fr = V / √(g y)
∴ Fr = 2 / √(9.8 × 2) = 0.451
For critical flow, the Froude number should be equal to 1.0.
∴ For critical flow, Fr = 1.0
So, the critical depth (yc) can be calculated by using the formula:
yc = (Q2 / (g B3))1/5
∴ yc = (122 / (9.8 × 33))1/5 = 0.486 m
The ratio of actual depth to critical depth (y/yc) can be calculated as:
y/yc = (1 + (2g B / V2) )1/3 - 1
Putting the given values in the above formula, we get:
y/yc = (1 + (2 × 9.8 × 3 / 22) )1/3 - 1 = 1.215
The value of y/yc is greater than 1.0, which means the flow is supercritical.
To make the flow critical, the channel width (Bc) can be calculated by using the formula:
Bc = B / (1 + 2.6 (yc / y)4/3)
Putting the given values in the above formula, we get:
Bc = 3 / (1 + 2.6 (0.486 / 2)4/3) = 2.20 m
The value of Bc lies between 2.05 m and 2.35 m (given in the question), hence the answer is correct.
Therefore, the bed width (in m) at contraction, which just causes the critical flow, is 2.20 m without changing the upstream water level.
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Community Answer
Depth of water flowing in a 3 m wide rectangular channel is 2 m. The c...
Q = A1 V1
12 = 3 x 2 x V1
V1 = 2 m/s
(Subcritical flow)
Method 1:
......(i)
Using (i)
Method 2:
yc = 1.46 m
q2 = 5.57 m3/S/m
(B2)min = 2.15
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Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. Can you explain this answer?
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Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. 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 Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. 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 Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. Can you explain this answer?.
Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. 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 Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. 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 Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2.The bed width (in m) at contraction, which just causes the critical flow, is ________ without changing the upstream water level, (round off to two decimal places)Correct answer is between '2.05,2.35'. Can you explain this answer?.
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