# Force exerted on Dam problem

1. Aug 23, 2011

### bcfcdan

1. The problem statement, all variables and given/known data

A vertical rectangular dam of width 25m contains water in a reservoir of depth 15m. What is the overall force exerted on the dam by the water?

2. Relevant equations

P=F/A .... F=PA
P = pgh

3. The attempt at a solution

I tried finding the Pressure (1000*9.807*15) and then multiplying that by area (15*25) but that doesn't give the right answer. Any tips would be much appreciated.

2. Aug 23, 2011

### Hootenanny

Staff Emeritus
Welcome to Physics Forums.

The reason that $F = \rho\cdot A$ does not give the correct answer is that the pressure varies with depth.

Does that help nudge you in the right direction?

3. Aug 23, 2011

### bcfcdan

Thanks for the reply, so I need to find the Pressure at each point along the Dam?

Which would be (1000 * 9.807 * 1) + (1000 * 9.807 * 2) .... up to 15m?

4. Aug 23, 2011

### Hootenanny

Staff Emeritus
You could do that, but it would be easier (and sufficient in this case) to find the average force on the damn.

5. Aug 23, 2011

### bcfcdan

Would that be (1000 * 9.807 * 7.5) * (15 * 25)?

Which gives 27,582kN

6. Aug 23, 2011

### Hootenanny

Staff Emeritus
Yup

7. Aug 23, 2011

### bcfcdan

Thanks for your help. Just looked at the answer that we were given for this question and it was 27,590kN.

8. Aug 23, 2011

### Hootenanny

Staff Emeritus
No problem.

You would have got exactly that answer if you'd have used $g=9.81\;\text{m}\cdot\text{s}^{-2}$.

9. Aug 23, 2011

### bcfcdan

Ah yes, I thought that might be it. Bit odd considering we get told to use g = 9.807 and then the correct answer is through using it as 9.81!