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A rectangular channel of 3m width carrying a discharge of 6m3/sec. If the specific Energy at depth (y1) is 20% more than specific Energy at critical depth, Then the depth of flow (y1) will be ________ m.
Take acceleration due to gravity to be 9.81 m/s2
Correct answer is '1.1-1.23'. Can you explain this answer?
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A rectangular channel of 3m width carrying a discharge of 6m3/sec. If ...
Concept:
Critical depth of flow:
q = discharge per unit width
Calculation:
Specific Energy at critical depth =
= 1.1122mSpecific Energy at depth “y1” = 1.20 Ec
E1 = 1.20 × 1.1122
E1 = 1.3347m
y1 = 1.191m
Most Upvoted Answer
A rectangular channel of 3m width carrying a discharge of 6m3/sec. If ...
Solution:
Given data:
- Width of the rectangular channel (B) = 3 m
- Discharge (Q) = 6 m3/s
- Specific energy at depth y1 = 1.2Ec (where Ec is the critical depth)
To find: Depth of flow (y1)
1. Calculation of critical depth (Ec):
Critical depth can be calculated using the following formula:
Ec = (Q2/gB2)1/3
where g = acceleration due to gravity (9.81 m/s2)
Plugging in the values, we get:
Ec = [(6)2/(9.81)(3)2]1/3 = 0.3 m
2. Calculation of specific energy at critical depth (Ec):
Specific energy at critical depth can be calculated using the following formula:
E = y + (Q2/2gA2)
where A = yB (cross-sectional area of flow)
At critical depth, y = Ec = 0.3 m and A = yB = (0.3)(3) = 0.9 m2
Plugging in the values, we get:
E = 0.3 + (62/2(9.81)(0.92)) = 1.54 m
3. Calculation of depth of flow (y1):
Given that specific energy at depth y1 = 1.2Ec
So, specific energy at depth y1 can be calculated as:
E = y1 + (Q2/2gA2)
where A = y1B (cross-sectional area of flow)
Plugging in the values, we get:
1.2Ec = y1 + (62/2(9.81)(y13))
Simplifying the equation, we get:
1.2(0.3 + (36/1.62y13)) = y1
Solving the equation, we get:
y1 = 1.1-1.23 m (approx.)
Therefore, the depth of flow (y1) is between 1.1 m to 1.23 m.
Given data:
- Width of the rectangular channel (B) = 3 m
- Discharge (Q) = 6 m3/s
- Specific energy at depth y1 = 1.2Ec (where Ec is the critical depth)
To find: Depth of flow (y1)
1. Calculation of critical depth (Ec):
Critical depth can be calculated using the following formula:
Ec = (Q2/gB2)1/3
where g = acceleration due to gravity (9.81 m/s2)
Plugging in the values, we get:
Ec = [(6)2/(9.81)(3)2]1/3 = 0.3 m
2. Calculation of specific energy at critical depth (Ec):
Specific energy at critical depth can be calculated using the following formula:
E = y + (Q2/2gA2)
where A = yB (cross-sectional area of flow)
At critical depth, y = Ec = 0.3 m and A = yB = (0.3)(3) = 0.9 m2
Plugging in the values, we get:
E = 0.3 + (62/2(9.81)(0.92)) = 1.54 m
3. Calculation of depth of flow (y1):
Given that specific energy at depth y1 = 1.2Ec
So, specific energy at depth y1 can be calculated as:
E = y1 + (Q2/2gA2)
where A = y1B (cross-sectional area of flow)
Plugging in the values, we get:
1.2Ec = y1 + (62/2(9.81)(y13))
Simplifying the equation, we get:
1.2(0.3 + (36/1.62y13)) = y1
Solving the equation, we get:
y1 = 1.1-1.23 m (approx.)
Therefore, the depth of flow (y1) is between 1.1 m to 1.23 m.
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A rectangular channel of 3m width carrying a discharge of 6m3/sec. If the specific Energy at depth (y1) is 20% more than specific Energy at critical depth, Then the depth of flow (y1) will be ________ m.Take acceleration due to gravity to be 9.81 m/s2Correct answer is '1.1-1.23'. Can you explain this answer?
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