# Estimating discharge at the outflow structure of a lake

## Main Question or Discussion Point

I am a fisheries biologist interested in manipulating a lake level by about six inches via a box cement outlet structure on a small lake. The outlet structure is currently governed by two adjacent 5ft by 0.5ft dam boards,which have historically been removed one at a time in the spring and replaced in the fall. However pulling whole boards releases too much water at once so I am trying to figure out whether incrementally lower boards would make a meaningful difference in Q.

As a starting point I am trying to figure out how much pressure is behind the 70 acre lake and what the average velocity (ft/sec) would be across the 2.5 square ft opening without the benefit of a flow meter. Is there a mathematical relationship between the impounded water and the velocity at the outlet? If there is then I could figure out the discharge for different square openings in the outlet structure, ie: cfs = ft/sec* length*width of the opening...

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tiny-tim
Homework Helper
Welcome to PF!

Hi salconflu! Welcome to PF!

Pressure depends only on depth, and not on horizontal area …

the pressure from the whole lake is exactly the same as the pressure at the same height in your bath.

From Bernoulli's equation the velocity is proportional to the square-root of the depth: v2 = 2ρgh.

And obviously the total flow is also proportional to the vertical area of the hole.