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A rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately?
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A rectangular channel 15 m wide has a normal depth of 0.8 m the dicsch...
Solution:
- Given:
- Width of the rectangular channel (b) = 15 m
- Normal depth (y) = 0.8 m
- Discharge (Q) = 10 m/s
- Formula used:
- Continuity equation: Q = A × V
- Manning's equation: V = (1/n) × (R^(2/3)) × (S^(1/2))
- Critical depth for rectangular channel: y_c = b/2
- Alternate depth for rectangular channel: y_a = (Q^2/(2g(b+y)^2))
- Specific energy equation: E = y + (V^2/(2g))
- Calculation:
- Area of flow (A) = b × y = 15 × 0.8 = 12 m²
- Velocity of flow (V) = Q/A = 10/12 = 0.833 m/s
- Hydraulic radius (R) = A/P, where P = b + 2y
R = A/P = 12/(15+1.6) = 0.727 m - Slope of the energy grade line (S) = (H_f/L), where H_f is the head loss and L is the length of the channel
Let's assume H_f = 0.05 m and L = 100 m (rough estimates)
S = 0.05/100 = 0.0005 - Manning's coefficient (n) for concrete channel = 0.013 (assumed)
- Using Manning's equation, substitute the values of R, S, and n:
V = (1/n) × (R^(2/3)) × (S^(1/2))
0.833 = (1/0.013) × (0.727^(2/3)) × (0.0005^(1/2))
Solving for R, we get R = 0.727 m - Since y < y_c="" (normal="" depth),="" the="" flow="" is="" subcritical="" and="" the="" alternate="" depth="" formula="" for="" rectangular="" channels="" is="" />
y_a = (Q^2/(2g(b+y)^2))
Substituting the values, we get y_a = 0.81 m (approx.) - To confirm that the alternate depth is correct, we can use the specific energy equation and compare the specific energies at normal and alternate depths:
E = y + (V^2/(2g))
At normal depth:
E_y = 0.8 + (0.833^2/(2×9.81))
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A rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately?
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A rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately? 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 rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately?.
A rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately? 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 rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular channel 15 m wide has a normal depth of 0.8 m the dicschrgecarries is 10 m/s the alternate depth will be approximately?.
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