Impact force on a falling object that spreads

[MelanieBrett]

Hi,

Homework Statement

I'm doing some research into the hydraulic jump and was wanting some help in calculating the impact force.
Hydraulic jump is a phenomenon to do with the turbulence of the water - it is the 'ring' around the stream of water when a tap is turned on

Homework Equations

The equation I have found to use is:
F = m g h / s

3. The Attempt at a Solution
I have the mgh, and was wondering what to use as the slow down distance.
I have been saying in my essay that the jump occurs when the water has slowed down enough. If that is my argument, then should I be using my values of the radius as the slow down distance?
Also, how should I be demonstrating it on a graph? Two of my experiments I wanted to compare were the height above the surface (h) and the density of water I was using (m) to see which affected the radius more. g is really the only constant, and there is no set variable (because I'm comparing two of them to see which affects the radius the most) - so what advice would you have?
Many many thanks, and I do apologise if this is a little incoherent; I'm quite tired and need to get this done soon :)
Update: Maybe if F were the gradient, then that would be easily comparable, so mgh on x-axis, and s on the y??

 

[haruspex]

Yes, I believe the radius is the point where the fast water has slowed to a critical value, where it matches the speed the wavefront would have on still water. (But since that speed would depend on the height of the jump, I'm not sure how one figures out exactly where that will be.)
In a channel it would be more straightforward, but in a ring the fast water is thinned as it spreads from the source. I suspect that means the water speed drops faster as it moves out, there being less thickness of water to maintain momentum against the constant drag. I.e., in regards to the equation you quote, F might increase with radius. (I'm thinking that your F is really a force per unit width of flow.) That would mean you need to integrate over the radius.