Question

COLLEGE PHYSICS QUESTION: Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 245 m2? Typical air density in Boulder is 1.14 kg/m3 , and the corresponding atmospheric pressure is 8.89 × 104 N/m2 . (Bernoulli’s principle assumes a laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.) please help!

Answer 1

ok lets start with the Bernoulli equation...what does is it?

Answer 2

\[P _{1}+1/2\rho v ^{2}=P _{2}+1/2\rho v ^{2}\]

Answer 3

how would you calculate the static pressure associated with the air moving at 45 m/s?

Answer 4

... I have no idea. Im so lost. I know that pressure is Force/area. but what is static pressure?

Answer 5

ok..if we assume the structure is closed (like a house) the air inside the house is stationary and has a pressure = to the atmospheric pressure. However, the moving air outside has a loer pressure.
Lets say the air inside is 1 and the air outside is 2. So
For 1, P1 = 8.89 *10^4 N/m^2
v1 = 0 (the air is essentially not moving

For 2
P2 = ?
V2 = 45 m/s

Now the density is assume to be constant for both 1 and 2.
Can you now solve for P2?

Answer 6

In the Bernoulli equation we refer to P1 and P2 as static pressures. The 1/2*rho*v^2 terms are called the dynamic pressures.

Answer 7

is the pressure in the house like regular atm pressure, or the atmospheric pressure that's provided?

Answer 8

It is the value provided in the problem which accounts for the fact Boulder is at altitude

Answer 9

ok. so then if the densities are constant can they be canceled out?

Answer 10

no, plug them in and you will see they can not be cancelled

Answer 11

I think im getting it. so is meters/second the correct unit to use In the equation? for v?

Answer 12

yes

Answer 13

ok so I set it up as 8.89*10^4+.5(1.14)(0^2m/s)=P2+.5(1.14)(45^2m/s)
right?

Answer 14

yes

Answer 15

remember the m/s units are also squared...(45 m/s) ^2

Answer 16

and then I multiply by the area to find the force?

Answer 17

not quite...P2 is the pressure pushing down on the roof but P1 is pushing up.
Since P1 is greater than P2 , the net force is up so:
(P1 - P1) * Area = net force....
draw a FBD to convince yourself this is coorect.

Answer 18

no I understand, it just didn't ask for net force, but I get it.

Answer 19

**(P1-P2)*Area
=)

Answer 20

Awesome!

Answer 21

oops for the typo...yes (P1 - P2) *area

Answer 22

yayyyyy I got it right ^-^ F=282791.25 N thank you!!

Answer 23

you are very welcome!