Question 367: 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 m
2
. 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 $$ 	imes $$ 10
5
N, upwards

Answer

2.4 $$ 	imes $$ 10
5
N, downwards

Answer

4.8  $$ 	imes $$ 10
5
N, downwards

Answer

4.8 $$ 	imes $$ 10
5
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 m 2 . 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: