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The hydraulic radius in the case of an open channel with great width is equal to
- a)Depth of channel
- b)1/2 x depth of channel
- c)1/3 x depth of channel
- d)1/4 x depth of channel
Correct answer is option 'A'. Can you explain this answer?
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The hydraulic radius in the case of an open channel with great width i...
Hydraulic Radius in Open Channel with Great Width
Definition of Hydraulic Radius:
Hydraulic radius is defined as the ratio of the cross-sectional area of the flow to the wetted perimeter of the channel.
Formula for Calculation of Hydraulic Radius:
Hydraulic radius (R) = A/P
Where A = Cross-sectional area of flow
P = Wetted perimeter of the channel
Case of Open Channel with Great Width:
In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel.
Explanation:
When the width of the channel is very large compared to the depth, the wetted perimeter of the channel becomes equal to the length of the channel. Therefore, the wetted perimeter is no longer dependent on the depth of the channel. As a result, the hydraulic radius is equal to the ratio of the cross-sectional area to the length of the channel which is equal to the depth of the channel.
Conclusion:
Hence, the correct option is A, i.e., the hydraulic radius in the case of an open channel with great width is equal to the depth of the channel.
Definition of Hydraulic Radius:
Hydraulic radius is defined as the ratio of the cross-sectional area of the flow to the wetted perimeter of the channel.
Formula for Calculation of Hydraulic Radius:
Hydraulic radius (R) = A/P
Where A = Cross-sectional area of flow
P = Wetted perimeter of the channel
Case of Open Channel with Great Width:
In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel.
Explanation:
When the width of the channel is very large compared to the depth, the wetted perimeter of the channel becomes equal to the length of the channel. Therefore, the wetted perimeter is no longer dependent on the depth of the channel. As a result, the hydraulic radius is equal to the ratio of the cross-sectional area to the length of the channel which is equal to the depth of the channel.
Conclusion:
Hence, the correct option is A, i.e., the hydraulic radius in the case of an open channel with great width is equal to the depth of the channel.
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The hydraulic radius in the case of an open channel with great width i...
Hydraulic Radius in Open Channel Flow
The hydraulic radius is an important parameter in fluid mechanics, particularly in the analysis of open-channel flow. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter. In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel. Let's understand this in more detail.
Definition of Hydraulic Radius
The hydraulic radius is a measure of the efficiency of a channel to convey water. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter. Mathematically, it can be expressed as:
Rh = A/Pw
where Rh is the hydraulic radius, A is the cross-sectional area of flow, and Pw is the wetted perimeter.
Hydraulic Radius in Open Channel Flow
In open-channel flow, the cross-sectional area of flow is the area of the water surface, and the wetted perimeter is the length of the channel bottom and sides in contact with the water. The hydraulic radius is an important parameter in the analysis of open-channel flow because it relates the flow rate to the water depth and channel shape.
In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel. This is because the wetted perimeter of such a channel is approximately equal to the width of the channel, and the cross-sectional area of flow is equal to the product of the width and depth.
Rh = A/Pw = (b x d) / (b + 2d) ≈ d
where b is the width of the channel and d is the depth of the channel.
Conclusion
In conclusion, the hydraulic radius is an important parameter in the analysis of open-channel flow. In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel. This relationship simplifies calculations and analysis of open-channel flow in wide channels.
The hydraulic radius is an important parameter in fluid mechanics, particularly in the analysis of open-channel flow. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter. In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel. Let's understand this in more detail.
Definition of Hydraulic Radius
The hydraulic radius is a measure of the efficiency of a channel to convey water. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter. Mathematically, it can be expressed as:
Rh = A/Pw
where Rh is the hydraulic radius, A is the cross-sectional area of flow, and Pw is the wetted perimeter.
Hydraulic Radius in Open Channel Flow
In open-channel flow, the cross-sectional area of flow is the area of the water surface, and the wetted perimeter is the length of the channel bottom and sides in contact with the water. The hydraulic radius is an important parameter in the analysis of open-channel flow because it relates the flow rate to the water depth and channel shape.
In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel. This is because the wetted perimeter of such a channel is approximately equal to the width of the channel, and the cross-sectional area of flow is equal to the product of the width and depth.
Rh = A/Pw = (b x d) / (b + 2d) ≈ d
where b is the width of the channel and d is the depth of the channel.
Conclusion
In conclusion, the hydraulic radius is an important parameter in the analysis of open-channel flow. In the case of an open channel with great width, the hydraulic radius is equal to the depth of the channel. This relationship simplifies calculations and analysis of open-channel flow in wide channels.
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The hydraulic radius in the case of an open channel with great width is equal toa)Depth of channelb)1/2 x depth of channelc)1/3 x depth of channeld)1/4 x depth of channelCorrect answer is option 'A'. Can you explain this answer?
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