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Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s?
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Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H...
Given information:
- Bed width (B) = 8 m
- Flow depth (y) = 3 m
- Side slope (Z) = 2H:1.5V
- Manning's rugosity coefficient (n) = 0.025
- Bed slope (S) = 1 in 10000
To find the velocity of the trapezoidal channel, we can use the Manning's equation:
V = (1/n) * (R^(2/3)) * (S^(1/2))
where V is the velocity, R is the hydraulic radius, n is the Manning's rugosity coefficient, and S is the bed slope.
Calculating the hydraulic radius (R):
- The hydraulic radius of a trapezoidal channel can be calculated as:
R = (A/P)
where A is the cross-sectional area of flow and P is the wetted perimeter.
Calculating the cross-sectional area (A):
- The cross-sectional area of a trapezoidal channel can be calculated as:
A = (B+y*Z)*y
where B is the bed width, y is the flow depth, and Z is the side slope.
Calculating the wetted perimeter (P):
- The wetted perimeter of a trapezoidal channel can be calculated as:
P = B + 2y*(1+Z^2)^(1/2)
Substituting the values into the equations:
A = (8+3*2/1.5)*3 = 42 m²
P = 8 + 2*3*(1+2^2)^(1/2) = 24.32 m
Calculating the hydraulic radius:
R = A/P = 42/24.32 = 1.727 m
Substituting the values into the Manning's equation:
V = (1/0.025) * (1.727^(2/3)) * (1/10000)^(1/2)
V = 40.96 * 0.0063
V = 0.257 m/s
Therefore, the velocity of the trapezoidal channel is approximately 0.257 m/s.
Answer: The correct option is (d) 0.9 m/s.
- Bed width (B) = 8 m
- Flow depth (y) = 3 m
- Side slope (Z) = 2H:1.5V
- Manning's rugosity coefficient (n) = 0.025
- Bed slope (S) = 1 in 10000
To find the velocity of the trapezoidal channel, we can use the Manning's equation:
V = (1/n) * (R^(2/3)) * (S^(1/2))
where V is the velocity, R is the hydraulic radius, n is the Manning's rugosity coefficient, and S is the bed slope.
Calculating the hydraulic radius (R):
- The hydraulic radius of a trapezoidal channel can be calculated as:
R = (A/P)
where A is the cross-sectional area of flow and P is the wetted perimeter.
Calculating the cross-sectional area (A):
- The cross-sectional area of a trapezoidal channel can be calculated as:
A = (B+y*Z)*y
where B is the bed width, y is the flow depth, and Z is the side slope.
Calculating the wetted perimeter (P):
- The wetted perimeter of a trapezoidal channel can be calculated as:
P = B + 2y*(1+Z^2)^(1/2)
Substituting the values into the equations:
A = (8+3*2/1.5)*3 = 42 m²
P = 8 + 2*3*(1+2^2)^(1/2) = 24.32 m
Calculating the hydraulic radius:
R = A/P = 42/24.32 = 1.727 m
Substituting the values into the Manning's equation:
V = (1/0.025) * (1.727^(2/3)) * (1/10000)^(1/2)
V = 40.96 * 0.0063
V = 0.257 m/s
Therefore, the velocity of the trapezoidal channel is approximately 0.257 m/s.
Answer: The correct option is (d) 0.9 m/s.
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Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s?
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Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s? 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 Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s?.
Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s? 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 Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Trapezoidal channel having bed width 8 m flow depth 3 m, side slope 2H : 1.5V.Manning's rugosity coefficent 0.025 and bed slope 1 in 10000, is having velocity of (a) 0.64m/s (b) 0.75 m/s (c) 1.05 m/s (d) O.9m/s?.
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