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Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005
- a)4.94×10-4 m
- b)5.94×10-4 m
- c)6.94×10-4 m
- d)7.94×10-4 m
Correct answer is option 'C'. Can you explain this answer?
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Calculate the rate of change of depth of a rectangular channel having ...
To calculate the rate of change of depth, we can use the Manning's equation:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Where:
Q = flow rate
n = Manning's roughness coefficient
A = cross-sectional area of the channel
R = hydraulic radius
S = slope of the channel
The cross-sectional area of the channel can be calculated by multiplying the depth (1m) by the width (4m):
A = 1m * 4m = 4m^2
The hydraulic radius can be calculated by dividing the cross-sectional area by the wetted perimeter. For a rectangular channel, the wetted perimeter is the sum of the width and twice the depth:
P = 4m + 2 * 1m = 6m
R = A / P = 4m^2 / 6m = 2/3 m
Given that the slope of the channel changes from S0 = 1/900 to Sf = 0.0005, we can calculate the rate of change of slope:
Rate of change of slope = (Sf - S0) / a = (0.0005 - 1/900) / a
Substituting the given values, we get:
Rate of change of slope = (0.0005 - 1/900) / a
The rate of change of depth can be calculated by rearranging the Manning's equation and solving for the flow rate:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Q = (1/40) * 4m^2 * (2/3 m)^(2/3) * S^(1/2)
Since the flow rate (Q) is constant, we can equate the two expressions for Q and solve for the rate of change of depth:
(1/40) * 4m^2 * (2/3 m)^(2/3) * S0^(1/2) = (1/40) * 4m^2 * (2/3 m)^(2/3) * Sf^(1/2) + (1/40) * 4m^2 * (2/3 m)^(2/3) * (0.0005 - 1/900) / a
Simplifying the equation:
(2/3 m)^(2/3) * S0^(1/2) = (2/3 m)^(2/3) * Sf^(1/2) + (2/3 m)^(2/3) * (0.0005 - 1/900) / a
Cancelling out the terms (2/3 m)^(2/3) from both sides:
S0^(1/2) = Sf^(1/2) + (0.0005 - 1/900) / a
Squaring both sides to isolate the rate of change of depth:
S0 = Sf + 2 * (0.0005 - 1/900) / a * Sf^(1/2) + (0.0005 - 1/900)^2 / a^2
Rearranging the equation to solve for the rate of change of depth:
Rate of
Q = (1/n) * A * R^(2/3) * S^(1/2)
Where:
Q = flow rate
n = Manning's roughness coefficient
A = cross-sectional area of the channel
R = hydraulic radius
S = slope of the channel
The cross-sectional area of the channel can be calculated by multiplying the depth (1m) by the width (4m):
A = 1m * 4m = 4m^2
The hydraulic radius can be calculated by dividing the cross-sectional area by the wetted perimeter. For a rectangular channel, the wetted perimeter is the sum of the width and twice the depth:
P = 4m + 2 * 1m = 6m
R = A / P = 4m^2 / 6m = 2/3 m
Given that the slope of the channel changes from S0 = 1/900 to Sf = 0.0005, we can calculate the rate of change of slope:
Rate of change of slope = (Sf - S0) / a = (0.0005 - 1/900) / a
Substituting the given values, we get:
Rate of change of slope = (0.0005 - 1/900) / a
The rate of change of depth can be calculated by rearranging the Manning's equation and solving for the flow rate:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Q = (1/40) * 4m^2 * (2/3 m)^(2/3) * S^(1/2)
Since the flow rate (Q) is constant, we can equate the two expressions for Q and solve for the rate of change of depth:
(1/40) * 4m^2 * (2/3 m)^(2/3) * S0^(1/2) = (1/40) * 4m^2 * (2/3 m)^(2/3) * Sf^(1/2) + (1/40) * 4m^2 * (2/3 m)^(2/3) * (0.0005 - 1/900) / a
Simplifying the equation:
(2/3 m)^(2/3) * S0^(1/2) = (2/3 m)^(2/3) * Sf^(1/2) + (2/3 m)^(2/3) * (0.0005 - 1/900) / a
Cancelling out the terms (2/3 m)^(2/3) from both sides:
S0^(1/2) = Sf^(1/2) + (0.0005 - 1/900) / a
Squaring both sides to isolate the rate of change of depth:
S0 = Sf + 2 * (0.0005 - 1/900) / a * Sf^(1/2) + (0.0005 - 1/900)^2 / a^2
Rearranging the equation to solve for the rate of change of depth:
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Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005a)4.94×10-4 mb)5.94×10-4 mc)6.94×10-4 md)7.94×10-4 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005a)4.94×10-4 mb)5.94×10-4 mc)6.94×10-4 md)7.94×10-4 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005a)4.94×10-4 mb)5.94×10-4 mc)6.94×10-4 md)7.94×10-4 mCorrect answer is option 'C'. Can you explain this answer?.
Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005a)4.94×10-4 mb)5.94×10-4 mc)6.94×10-4 md)7.94×10-4 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005a)4.94×10-4 mb)5.94×10-4 mc)6.94×10-4 md)7.94×10-4 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the rate of change of depth of a rectangular channel having depth 1m and width 4m. Given: C = 40, S0 = 1/900, Sf = 0.0005a)4.94×10-4 mb)5.94×10-4 mc)6.94×10-4 md)7.94×10-4 mCorrect answer is option 'C'. Can you explain this answer?.
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