# Homework Help: Bernoulli/Pascal Tarpaulin Problem

1. Nov 16, 2007

### Romanian

Bernoulli/Pascal "Tarpaulin" Problem

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

"The construction of a flat rectangular roof (4.0m x 5.5m) allows it to withstand a maximum net outward force of 21 000 N. The density of the air is 1.29 kg/m^3. At what wind speed will this roof blow outward?"

A1=22m^2
F=21000 N
p=1.29
v1=0?

2. Relevant equations

Bernoulli's Equation:
P1-1/2p(v1)^2+pgy1=P2+1/2(v2)^2+pgy2

Pascal's Principle?
F2=F1*(A2/A1)

3. The attempt at a solution

1/2(1.29)v1^2=1/2(1.29)v2^2

I believe this has something to do with Pascal's Principle, but I'm not quite sure.

2100=F1(A2/22)

From here, I'm completely lost.

On a side note, I have a quick question on Archimedes' Principle. The weight of the displaced fluid is normally found through the volume of the displaced fluid and the given density, correct?

2. Nov 16, 2007

### Shooting Star

The wind is blowing at a speed of v. Think of a volume of air with cross-sectional area A and length vt, which is adjacent to the wall of area A and blowing toward the wall. In exactly time t, all of this air would collide with the wall, and impart its momentum to the wall. The momentum of the air after collision is zero in the direction it was blowing, because it will disperse horizontally after hitting the wall. (This may not be exactly true, but we have to idealise the situation.) So,

Change in momentum of this air = Mass of this air*(difference in initial and final velo)
= impulse given to the wall in time t
=>
(Vol of air)*(density of air)*v = F*t, where vol of air is vt.

Plug in the numbers to get the force.

What you asked in the side note is also correct. It can also be found if you know the weight of the object floating in the liquid.