Bernoulli's equation for hurricane wind pressure on a roof

[gamergirlxoxox]

3) Hurricane Michael had horizontal winds of V_out = 69 m/s (155 mph). P_air = 1.29 kg/m³. A building with a flat, horizontal roof, A_roof = 200 m², and V_in = 0 m/s.

a) What is the pressure difference, P_in - P_out on the roof. Assume Y_in = Y_out.

b) What is the force acting on the roof, and what is the direction of this force ?

c) What is this force in pounds ? 1 N = .225 lb.

After the storm, it is found that a small object has been driven into the water tower. The water level inside the water tower is 12 meters above the ground. The height of the hole is 9 meters above the ground. The object is removed and water sprays out.

d) Considering the hole and the tower, what is the speed of the water coming out of the hole ? Assume V_in = 0 and P_in = P_out = P_atm.

e) If the hole is 9 meters above the ground, how long does it take the water to hit the ground ?

f) With the speed the water has, and the time to hit the ground, how far does it travel horizontally ?

So, I'm not sure if I did it right but what I did for part A was use the Bernoulli's equation:

P₁ + 1/2pv₁= P₂ + 1/2pv₂

Delta P (P2-P1)= 1/2pv²₁ - 1/2pv²₂

Delta P = 1/2p (V²₁ - V²₂)

Delta P = 1/2 (1.29 kg/m³) (69² m/s - 0² m/s)

Delta P = 3070 PA

I'm not sure if I'm correct though so I didn't really attempt to do the other questions to this problem in case I'm wrong.. I'll gladly appreciate it if someone could help me out.

 

[I like Serena]

Hey gamergirlxoxox! Welcome to MHB! ;)

You are entirely correct.

Here's a video where it's explained:
[YOUTUBE]cUMspps8d8A[/YOUTUBE]

 

[gamergirlxoxox]

Thanks ! I think I can probably figure the rest out now