Change in Stream Velocity

I think that all really depends on the geometry of the river. If you need to push the same volume through a smaller opening, the velocity will increase. In the same regard, if you allow gravity to act on the velocity of the water to a higher degree than it does before the elevation drop, the velocity will increase 9.8m/s^2. But there are many factors at play such as turbulence, obstructions, changes in flow path etc etc etc which would not really make it feasible to figure the velocity using math. I would think that you would need to take empirical measurements if you want to know the numbers.

You could get a theoretical value based on a list of assumptions if you desire. You can calculate just about anything you wish... But you should ask yourself "why?"

This is homework. You should remember that elevation change is what makes the water flow. Without it, you'd have a lake.

Reynolds number - Wikipedia, the free encyclopedia

Thanks--that's a good / helpful answer.

So, assuming that the cross-sectional area of the stream doesn't change after the sudden drop, the velocity doesn't change.

Now, if that sudden drop is sudden enough (i.e., a waterfall), I suppose that while the water is falling it increases velocity (in a vertical direction), but once it has fallen (or shortly after it has fallen) it will lose that vertical component of velocity and return to the (horizontal) speed before the fall (assuming the cross section of the stream hasn't changed).

(And this ignores a pool that might form under the waterfall where the cross section is larger--I guess I could think of the cross section of the stream returning to its original size somewhere a little way downstream of any such pool.)

(Oh, and just for the record, I'm not the OP, just found it kind of interesting to think about--at first I was thinking it had to pick up a lot of velocity during that elevation change, and it probably does, short term. But, assuming the stream cross section returns to the same cross section as before the drop, the velocity should return to what it was above. Of course, as another poster pointed out, you really need to make a physical measurement to find the velocity, as we don't know what the cross section is downstream of the elevation drop.)

Wow,

If it all added up, the stream would vaporize and become steam.

Cross section here (in a stream) is difficult to define. A better definition is: If the stream has the same width and slope as before the fall, then the flow speed remains the same. if the slope changes for the same width (equivalent to changing the cross section), then there will be change in flow speed.

I would recommend you become familiar with the Bernoulli equation. It's essential for anyone dealing with fluids. And, it will answer your question.

If a lake has both an inlet and an outlet, it is basically just a wide spot in a river. To maintain flow, the inlet end must be higher than the outlet end, albeit by a virtually undetectable amount. I wonder if Hydrology 101 addresses this....

Excusing the pun, maybe we could organize a pool on this. For Lake Roosevelt (150 miles backed up behind Grand Coulee Dam), would the upper end be 0.001, 0.01, 0.1, 1.0, 10.0, or 100.0 inches higher than the lower end? Inquiring minds wanna know!

If velocity increases, flow rate has to increase. Since incoming flow is fixed any increased flow will lead to depletion of the stream, which is not possible in steady state flow. If the velocity increases, the depth will decrease to keep volume rate constant. In any case this will be a local disturbance and will settle down in a short distance.

Bioramani

Here are some relationships that might help solve your problem:

The velocity of the water is inversely proportional to the cross section. Assuming a constant width, it will be inversely proportional to the depth. The hydrostatic pressure is proportional to the depth and the rate of change of water velocity is proportional to the difference in hydrostatic pressure upstream and downstream, i.e. the slope of the water surface. As the water approaches the waterfall, the level decreases due to lower hydrostatic pressure on the downstream side and the velocity increases. In the end, the velocity increase is limited by the viscosity, the flow becomes turbelent, so there is a minimum depth and maximum velocity right at the waterfall.