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The most economical section of a trapezoidal channel is one which has hydraulic mean depth equal to
- a)1/2 depth
- b)1/2 breadth
- c)1/2 sloping side
- d)1/4 (depth + breadth)
Correct answer is option 'A'. Can you explain this answer?
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The most economical section of a trapezoidal channel is one which has ...
Introduction:
In the field of hydraulics, the design of open channels plays a crucial role. A trapezoidal channel is a commonly used shape due to its stability and efficiency in carrying water. The most economical section of a trapezoidal channel refers to the cross-sectional shape that minimizes the cost of construction and maintenance while efficiently carrying the desired flow.
Explanation:
To determine the most economical section of a trapezoidal channel, we need to consider the hydraulic mean depth (HMD). The hydraulic mean depth is defined as the ratio of the cross-sectional area to the wetted perimeter of the channel.
Hydraulic Mean Depth (HMD) Formula:
HMD = (cross-sectional area) / (wetted perimeter)
To minimize the cost of construction and maintenance, we want to minimize the wetted perimeter. The wetted perimeter is the total length of the channel boundary in contact with water.
Analysis of Options:
a) 1/2 depth: If the hydraulic mean depth is equal to half the depth, it means that the cross-sectional area is maximized for a given wetted perimeter. This results in a more efficient flow and minimizes the cost of construction and maintenance. Therefore, option 'A' is correct.
b) 1/2 breadth: The breadth of the trapezoidal channel does not directly affect the hydraulic mean depth. It is possible to have a channel with a large breadth but a low hydraulic mean depth. Therefore, option 'B' is incorrect.
c) 1/2 sloping side: The hydraulic mean depth is not directly related to the sloping sides of the channel. The slope of the sides affects the overall stability of the channel but does not determine its economy. Therefore, option 'C' is incorrect.
d) 1/4 (depth x breadth): The hydraulic mean depth is not directly proportional to the product of depth and breadth. It is possible to have a channel with a low hydraulic mean depth even if the product of depth and breadth is high. Therefore, option 'D' is incorrect.
Conclusion:
The most economical section of a trapezoidal channel is the one in which the hydraulic mean depth is equal to half the depth. This ensures that the cross-sectional area is maximized for a given wetted perimeter, resulting in efficient flow and minimizing the cost of construction and maintenance.
In the field of hydraulics, the design of open channels plays a crucial role. A trapezoidal channel is a commonly used shape due to its stability and efficiency in carrying water. The most economical section of a trapezoidal channel refers to the cross-sectional shape that minimizes the cost of construction and maintenance while efficiently carrying the desired flow.
Explanation:
To determine the most economical section of a trapezoidal channel, we need to consider the hydraulic mean depth (HMD). The hydraulic mean depth is defined as the ratio of the cross-sectional area to the wetted perimeter of the channel.
Hydraulic Mean Depth (HMD) Formula:
HMD = (cross-sectional area) / (wetted perimeter)
To minimize the cost of construction and maintenance, we want to minimize the wetted perimeter. The wetted perimeter is the total length of the channel boundary in contact with water.
Analysis of Options:
a) 1/2 depth: If the hydraulic mean depth is equal to half the depth, it means that the cross-sectional area is maximized for a given wetted perimeter. This results in a more efficient flow and minimizes the cost of construction and maintenance. Therefore, option 'A' is correct.
b) 1/2 breadth: The breadth of the trapezoidal channel does not directly affect the hydraulic mean depth. It is possible to have a channel with a large breadth but a low hydraulic mean depth. Therefore, option 'B' is incorrect.
c) 1/2 sloping side: The hydraulic mean depth is not directly related to the sloping sides of the channel. The slope of the sides affects the overall stability of the channel but does not determine its economy. Therefore, option 'C' is incorrect.
d) 1/4 (depth x breadth): The hydraulic mean depth is not directly proportional to the product of depth and breadth. It is possible to have a channel with a low hydraulic mean depth even if the product of depth and breadth is high. Therefore, option 'D' is incorrect.
Conclusion:
The most economical section of a trapezoidal channel is the one in which the hydraulic mean depth is equal to half the depth. This ensures that the cross-sectional area is maximized for a given wetted perimeter, resulting in efficient flow and minimizing the cost of construction and maintenance.
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