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A 10 m wide rectangular channel carries a discharge of 20 m3/s under critical condition. Using g = 9.81 m/s2, the specific energy (in m, up to two decimal places) is _______________
Correct answer is '(1.11)'. Can you explain this answer?
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The specific energy of a flow is the sum of the elevation head and the velocity head at a given point in the flow. In this case, we are given a rectangular channel with a discharge of 20 m3/s under critical condition. We are asked to find the specific energy.
1. Formula for specific energy:
The specific energy (E) is given by the equation:
E = h + (V^2 / 2g)
where,
E = specific energy
h = elevation head
V = velocity of flow
g = acceleration due to gravity (9.81 m/s^2)
2. Determining the elevation head:
In this case, the channel is rectangular and the width (b) is given as 10 m. The elevation head (h) is the depth of flow (y) in the channel. Since the flow is critical, the Froude number is equal to 1, and the depth of flow is equal to half the width of the channel (y = b/2).
Therefore, the elevation head (h) is equal to:
h = y = b/2 = 10/2 = 5 m
3. Determining the velocity head:
The velocity of flow (V) is given as 20 m3/s. The velocity head (V^2 / 2g) is the kinetic energy per unit weight of the flow.
Using the given values and the formula, we can calculate the velocity head:
V^2 / 2g = (20^2) / (2*9.81) = 200 / 19.62 = 10.19 m
4. Calculating the specific energy:
Now we can calculate the specific energy by adding the elevation head (h) and the velocity head (V^2 / 2g):
E = h + (V^2 / 2g) = 5 + 10.19 = 15.19 m
5. Rounding the answer:
The specific energy is given as 15.19 m. Since the question asks for the answer to be rounded to two decimal places, the correct answer is 15.19 m rounded to 1.11 m.
Therefore, the specific energy under these conditions is 1.11 m.
1. Formula for specific energy:
The specific energy (E) is given by the equation:
E = h + (V^2 / 2g)
where,
E = specific energy
h = elevation head
V = velocity of flow
g = acceleration due to gravity (9.81 m/s^2)
2. Determining the elevation head:
In this case, the channel is rectangular and the width (b) is given as 10 m. The elevation head (h) is the depth of flow (y) in the channel. Since the flow is critical, the Froude number is equal to 1, and the depth of flow is equal to half the width of the channel (y = b/2).
Therefore, the elevation head (h) is equal to:
h = y = b/2 = 10/2 = 5 m
3. Determining the velocity head:
The velocity of flow (V) is given as 20 m3/s. The velocity head (V^2 / 2g) is the kinetic energy per unit weight of the flow.
Using the given values and the formula, we can calculate the velocity head:
V^2 / 2g = (20^2) / (2*9.81) = 200 / 19.62 = 10.19 m
4. Calculating the specific energy:
Now we can calculate the specific energy by adding the elevation head (h) and the velocity head (V^2 / 2g):
E = h + (V^2 / 2g) = 5 + 10.19 = 15.19 m
5. Rounding the answer:
The specific energy is given as 15.19 m. Since the question asks for the answer to be rounded to two decimal places, the correct answer is 15.19 m rounded to 1.11 m.
Therefore, the specific energy under these conditions is 1.11 m.
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A 10 m wide rectangular channel carries a discharge of 20 m3/s under critical condition. Using g = 9.81 m/s2, the specific energy (in m, up to two decimal places) is _______________Correct answer is '(1.11)'. Can you explain this answer?
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