How Does Downstream Restriction Affect Upstream Water Levels in Fluid Mechanics?

[Vishesh]

Dear Friends,
I need some ideas on a problem I am facing at work. I have attached a sheet with has a rough picture of scenario. I urge you to please keep open the picture while reading my problem.
Problem:- There is a small wall in a water stream. Due to the small wall the water stream upside of the wall gets a height of H1 while after falling from the small wall it gets a height of H2. As you can see in the picture the height of water down stream is lesser than the height of the small wall.
Now the condition is changed.
Somewhere in the down stream we made created some restriction which caused rise in the downstream water level i.e. H3. This H3 height is higher than height of the wall, let's say it generates delta h difference.
Discharge Q is same. Consider there is no changes in Area.
Now my question is that if this situation happens what will be its effect on the water height at upstream? Will upstream level H1 change to H4 which will be higher than H1, or will it remain same until the two water level matches with each other.

 

[256bits]

Your wall is usually called a weir, or a spillway.
A properly designed weir will not increase the upstream height of the flow, but since the river flow does vary throughout the season, the fixed weir height is fixed, that is more of a theoretical consideration, since at times the weir will be too low ( high volume water flow in spring or after rain ) or too high ( dry seasons ).
( A dam increases the upstream level of the river )

The weir functions either as free flow or submerged.

You are asking if by being submerged whether the downstream level of the water has an effect upon the upstream level.
This depends upon the type of weir.
A broad crest weir can still be considered as having free flow when the ratio of downstream level h2 to upstream level h1 is less than about 0.7.
For a sharp crested weir the ratio h2/h1 is around 0.2 or less for free flow.
Other weir shapes would have different values.
h1 and h2 are measured from the top (crest ( of the weir ) for slow moving water. If the upstram velocity of the water is fast, h1 will include the kinetic energy head of the water.

So as long as you have not exceeded the h2 height, and the ratio h2/h1, respective to your weir, you can asssume free flow and the downstream level will not affect the upstream level.

these give some info.
http://irrigationtoolbox.com/NEH/TechnicalNotes/DesignNotes/DN-15.pdf
and
http://www.jfccivilengineer.com/broad_crested_weir.htm

 

[Vishesh]

Thanks a lot for reply friend.
Have few questions though.
These h1 & h2 height you are saying is from the top of crest, right? so it means that the downstream flow can be of any height irrespective of height of spillway and it will not disturb water height of upstream side until the ration of h2 to h1 crosses 0.7.
And when this ratio crosses 0.7 the water level height at upstream will increase. is it right?
I would highly appreciate if you again give some more clarification.