# Water pressure and explosions

1. Feb 20, 2008

### qubert

m studying civil engineering and trying to research how a bomb would affect a dam, but i know little about physics so could anyone help with this problem?

dam has dimensions 7.6m wide at the top, 39.6m wide at the bottom and 34m tall, water level is 2m from top of the dam.

135*10^6 cubic metres of water behind dam

bomb explodes at a depth of 9m and creates a pressure of 100kN/m^2 over the back of the dam in addition to the water,

how would i draw a graph to represent the pressure behind the dam?

many thanks..

2. Feb 20, 2008

### Q_Goest

Hi qubert,
Do you know how to find pressure on the dam as a function of depth?
From the way this is worded, I read this to mean only that the bomb creates a pressure of 100 kN/m^2 over the entire face of the damn (all over). Unless there is some additional information (such as how far away from the dam the bomb explodes and the pressure is 100 kN/m^2 at some given radius) then I think we have to assume the pressure is superimposed on top of the pressure you find as a function of depth.

3. Feb 21, 2008

### qubert

is it just force*area?

4. Feb 21, 2008

### rohanprabhu

actually.. it's Force/Area.. but the thing here is more complicated than that. For an explosion, the damaging 'shock waves' generally travel via compressions and rarefactions in the air accompanied by shrapnel. The thing is that when you use the formula Force/Area, you can directly substitute variables only if the Force is uniform over the complete area, which in our case is not because the shockwaves travel radially outwards (as a generalization) and hence depending on where the bomb exploded.. the force will be different at different areas and hence the pressure. So, for your case, pressure is rather the derivative of force with respect to area:

$$P = \frac{dF}{dA}$$

5. Feb 21, 2008

### qubert

so to create this graph i would use this equation to find the pressure of 100kn and at each 1m and add the pressure of the water using pressure=water density*gravity*depth?, would it make any difference to the 2m of the dam protruding out of the water or the changing thickness of the dam? thanks

6. Feb 21, 2008

### rohanprabhu

$$P = \rho_w mgh$$

is the pressure for a surface when gravity acts parallel to the application of force to it. You need the pressure for the wall of a dam, where gravity is perpendicular to the wall.

Also, a graph is drawn between two variables to show how they vary with each other. I'm not at all clear which graph you are talking about when you say that you want to 'draw a graph of pressure'. It has to be Pressure vs. something.

Can you please be clear on '2m of the dam protruding out of the water'. Changing the thickness of the dam walls will increase the yield strength. However it needs to be done keeping elastic properties in mind else despite an increase yield strength, the ability of the walls to withstand the shockwave will decrease.

Also, 'pressure of 100 kN/m^2' doesn't mean anything because as i said.. in the case of a bomb the pressure in bomb is not constant at a given area. It is different at different areas.

If you are dealing with a word problem from a textbook or something.. it'd be helpful if you quote the entire problem.

7. Feb 21, 2008

### qubert

Theb bouncing bomb was designed to explode at a depth of 9m below the surface. The dam itself, had the dimensions shown below.

7.6m wide at top
39.6m wide at bottom
34m height
135x10^6m^3 of water behind dam
bomb sinks and explodes against wall at 9m depth

If the explosion developed a pressure of 100 kN/m2 over the back of the Dam in addition to the pressure from the water; draw a graph of the pressure behind the dam if the distance from water surface to top of dam is 2m. (Assume back of Dam to be vertical).

is the problem, thanks

i think by draw a graph it just means plot how the the pressure increases with depth? starting with 0 when the dam is out of the water getting higher with water pressure + the explosion?