Impact Force of a falling object causing it to spread out

[MelanieBrett]

Hi,
I'm doing some research into the hydraulic jump and was wanting some help in calculating the impact force. The equation I have found to use is:
F = m g h / s
I have the mgh, and was wondering what to use as the slow down distance.
If you didn't know what the hydraulic jump was, it 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. 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??

 

[davenn]

something I had never heard of before, tho well aware of the phenomenon
From wiki, a pic for those unfamiliar with the term ...

Figure 2: A common example of a hydraulic jump is the roughly circular stationary wave that forms around the central stream of water. The jump is at the transition between the point where the circle appears still and where the turbulence is visible.

MelanieBrett
have you looked at the wiki page ?
https://en.wikipedia.org/wiki/Hydraulic_jump

dunno if amongst that mass of formulae there is something that answers your Q's ??
its a bit deep for me ( excuse the pun)
Dave

 

[Andy Resnick]

Hi,
I'm doing some research into the hydraulic jump and was wanting some help in calculating the impact force. <snip>

First, a semi-major quibble: there is no such thing as "impact force". That phrase needs to be removed from your vocabulary as it reflects pre-Newtonian concepts.

Now- hydraulic jumps. My colleague Jearl Walker's book "Flying Circus of Physics" has a nice discussion about this. The phenomenon is analogous to an atmospheric shock wave. The ratio of fluid velocity to gravity wave velocity is called the Froude number:

https://en.wikipedia.org/wiki/Froude_number

The Froude number is very useful- not just for ship hull design but also analysis of swimming and walking.

The hydraulic jump occurs when the Froude number drops below 1. Inside the jump, the fluid is shallow and the flow supercritical (Fr >1). Outside the jump, the fluid is thicker and the flow subcritical (Fr <1). The jump itself marks the boundary Fr = 1.