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# Rivers and Hydraulic Radius watch

1. Ok I am a little confused, I though that efficiency increased downstream? Am I right in thinking that hydraulic radius decreases downstream because of the larger wetted perimeter? The lower hydraulic radius means that river would be less efficient right but I thought that efficiency increased downstream?

As in an past exam question it said the HR was 0.13 in the upper course and 0.10 in the lower course so efficiency is lower in the lower course!

I am so confused...
2. The hydraulic radius increases further downstream, as does the wetter perimeter (have a look at something called the Bradshaw Model )

The flow efficiency thus also increases, because:
Hydraulic radius = Cross-sectional Area/ Wetted Perimeter

So if the hydraulic radius has increased downstream, what we are saying is that if we look at a cross-section, a lower ratio of the water in the cross-section is in contact with the bed and banks (wetted perimeter) than it was further upstream. Less contact with bed and banks makes for reduced friction, which in turn makes for a more efficient river flow.

Uth =]
3. (Original post by uthred50)
The hydraulic radius increases further downstream, as does the wetter perimeter (have a look at something called the Bradshaw Model )

The flow efficiency thus also increases, because:
Hydraulic radius = Cross-sectional Area/ Wetted Perimeter

So if the hydraulic radius has increased downstream, what we are saying is that if we look at a cross-section, a lower ratio of the water in the cross-section is in contact with the bed and banks (wetted perimeter) than it was further upstream. Less contact with bed and banks makes for reduced friction, which in turn makes for a more efficient river flow.

Uth =]
Thanks! Does this sound about right?

In the upper course, the channel is narrow and rough, there is a large wetted perimeter due to lots of boulders/rocks etc. The wetted perimeter is the total length of the bed and banks of the river in contact with water. When there is a large wetted perimeter in relation to the amount of discharge in the river, there is more friction which reduces the velocity of the river. The river is less efficient.

In the middle and lower course the channel becomes larger and smoother (less rough), this makes the river more efficient. The wetted perimeter is proportionately smaller than the amount of discharge in the channel. Therefore there is less friction to reduce velocity. The river is more efficient.

The hydraulic radius is the cross sectional area / wetted perimeter. It is a measure of efficiency. A high HR means that the river is more efficient. This is because there is a smaller proportion of water in contact with the wetted perimeter so friction is lower which increases velocity. However one must take into account that in the upper course there is more energy lost due to friction with a rough channel which decreases efficiency.
4. (Original post by lucasluke)
Thanks! Does this sound about right?

In the upper course, the channel is narrow and rough, there is a large wetted perimeter due to lots of boulders/rocks etc. The wetted perimeter is the total length of the bed and banks of the river in contact with water. When there is a large wetted perimeter in relation to the amount of discharge in the river, there is more friction which reduces the velocity of the river. The river is less efficient.

In the middle and lower course the channel becomes larger and smoother (less rough), this makes the river more efficient. The wetted perimeter is proportionately smaller than the amount of discharge in the channel. Therefore there is less friction to reduce velocity. The river is more efficient.

The hydraulic radius is the cross sectional area / wetted perimeter. It is a measure of efficiency. A high HR means that the river is more efficient. This is because there is a smaller proportion of water in contact with the wetted perimeter so friction is lower which increases velocity. However one must take into account that in the upper course there is more energy lost due to friction with a rough channel which decreases efficiency.
The wetted perimeter isn't necessarily large upstream; in fact it's usually much lower than downstream because upstream channels are relatively small. What is important is the hydraulic radius, which represents the ratio of bed and banks to cross-sectional water flow (discharge), and which tends to get larger further downstream. The wetted perimeter is the total length of bed and banks in contact with the water in any given cross-section .

Rather than having your separate bit at the end about hydraulic radius, include it earlier when you say 'When there is a large wetted perimeter in relation to the amount of discharge in the river, there is more friction which reduces the velocity of the river.' You are describing hydraulic radius here, so no need to repeat it all again later!

Uth

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