Critical v. normal depth problem

Here's a sample problem from the PPI site. They just give the equation to solve it with no explanation of the theory, I was hoping someone could enlighten me.

The equation btw, is not in the CERM as far as I have found.

"The height of a submerged barrier placed across the entire width of a 15 ft wide rectangular channel can be increased or decreased according to varying flow conditions. At a flow velocity of 3 ft/sec and a normal depth of 8 ft, how high can the barrier be raised before creating a change in the water depth upstream of the barrier?"

So you're trying to solve for the critical depth above the barrier, whose total height (critical depth and barrier height added together) is equal to the normal depth so that you get normal depth = critical depth, flow is critical, and no there's no change in upstream depth?

The answer is 4.2'

Thanks!

Environmental_Guy said:

Here's a sample problem from the PPI site. They just give the equation to solve it with no explanation of the theory, I was hoping someone could enlighten me.
The equation btw, is not in the CERM as far as I have found.

"The height of a submerged barrier placed across the entire width of a 15 ft wide rectangular channel can be increased or decreased according to varying flow conditions. At a flow velocity of 3 ft/sec and a normal depth of 8 ft, how high can the barrier be raised before creating a change in the water depth upstream of the barrier?"

So you're trying to solve for the critical depth above the barrier, whose total height (critical depth and barrier height added together) is equal to the normal depth so that you get normal depth = critical depth, flow is critical, and no there's no change in upstream depth?

The answer is 4.2'

Thanks!

Click to expand...

Controls in subcritical channels affect upstream hydraulics. You are looking at a depth that flow becomes supercritical so it can no longer affect upstream. Sorry i don't have books with em at work to look up for an equation.

E1= E2

E =d + v^2/2g

d1 = 8'

v1 = 3 ft/sec

d2 = barrier ht + rect. channel crit. depth

v2 is based on crit. depth

Solve for barrier ht.

CERM eqns. 19.66 and 19.74

See example 19.7, 10th CERM