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A rectangular channel is 5 m wide and 3 m deep. Water is flowing in the channel for a depth of 2.5 m. The hydraulic radius is
- a)0.50
- b)1.25
- c)2.00
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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A rectangular channel is 5 m wide and 3 m deep. Water is flowing in th...
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A rectangular channel is 5 m wide and 3 m deep. Water is flowing in th...
Hydraulic radius (R) is a parameter used in fluid mechanics to characterize the flow of water in open channels. It is defined as the ratio of the cross-sectional area of flow (A) to the wetted perimeter (P) of the channel.
To find the hydraulic radius in this rectangular channel, we need to calculate the cross-sectional area and wetted perimeter.
Cross-sectional area (A):
The cross-sectional area of the flow can be calculated by multiplying the width of the channel (5 m) by the depth of the flow (2.5 m).
A = width × depth
A = 5 m × 2.5 m
A = 12.5 m²
Wetted perimeter (P):
The wetted perimeter is the sum of all the sides that come into contact with the water. In a rectangular channel, the wetted perimeter is given by the sum of the width and two times the depth.
P = width + 2 × depth
P = 5 m + 2 × 2.5 m
P = 5 m + 5 m
P = 10 m
Hydraulic radius (R):
Now, we can calculate the hydraulic radius by dividing the cross-sectional area (A) by the wetted perimeter (P).
R = A / P
R = 12.5 m² / 10 m
R = 1.25 m
The hydraulic radius of the rectangular channel is 1.25 m. Therefore, the correct answer is option (B) 1.25.
To find the hydraulic radius in this rectangular channel, we need to calculate the cross-sectional area and wetted perimeter.
Cross-sectional area (A):
The cross-sectional area of the flow can be calculated by multiplying the width of the channel (5 m) by the depth of the flow (2.5 m).
A = width × depth
A = 5 m × 2.5 m
A = 12.5 m²
Wetted perimeter (P):
The wetted perimeter is the sum of all the sides that come into contact with the water. In a rectangular channel, the wetted perimeter is given by the sum of the width and two times the depth.
P = width + 2 × depth
P = 5 m + 2 × 2.5 m
P = 5 m + 5 m
P = 10 m
Hydraulic radius (R):
Now, we can calculate the hydraulic radius by dividing the cross-sectional area (A) by the wetted perimeter (P).
R = A / P
R = 12.5 m² / 10 m
R = 1.25 m
The hydraulic radius of the rectangular channel is 1.25 m. Therefore, the correct answer is option (B) 1.25.
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A rectangular channel is 5 m wide and 3 m deep. Water is flowing in the channel for a depth of 2.5 m. The hydraulic radius isa)0.50b)1.25c)2.00d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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