Question 344: Properties of Matter

Question

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $$({\rho _{air}} = 1.2kg/{m^3})$$

Accepted Answer

Using Bernoulli's theorem and assuming density constant,
P
1
+1/2ÃÂv
1
2
= P
2
+1/2ÃÂv
2
2
where:
P
2
= pressure outside house
P
1
= pressure inside house
v
1
= speed of air inside house
v
2
= speed of air outside house
Pressure difference,
P
1
Ã¢ÂÂ P
2
= 1/2ÃÂ	[v
2
2
Ã¢ÂÂ v
1
2
]
Now,  P
1
Ã¢ÂÂ P
2
= 1/2 ÃÂ 1.2 [40
2
Ã¢ÂÂ 0
2
]
P
1
Ã¢ÂÂ P
2
= 960 N/m
2
Since Pressure P = Force/Area, so force acting on roof will be :
F = P ÃÂ A
F = 960 ÃÂ 250
F = 960 ÃÂ 1000/4
F = 24ÃÂ10
4
or 2.4ÃÂ10
5
N
which is acting upward.

Answer

2.4 $$ 	imes $$ 105 N, upwards

Answer

2.4 $$ 	imes $$ 105 N, downwards

Answer

4.8  $$ 	imes $$ 105 N, downwards

Answer

4.8 $$ 	imes $$ 105 N, upwards

Properties of Matter

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho _{air}} = 1.2kg/{m^3})

Choose the correct answer: