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:

(Pair=1.2kg/m3)

  • Option 1)

    2.4 x 105 N, upwards

  • Option 2)

    2.4 x 105 N, downwards

  • Option 3)

    4.8 x 105 N, downwards

  • Option 4)

    4.8 x 105 N, upwards

 

Answers (1)

As we learnt in

Bernoulli's Principle -

The total energy (Pressure energy, Potential energy and Kinetic energy ) per unit volume or mass of an incompressiable and non viscous fluid in steady flow through a pipe remains constant.

- wherein

P+\rho gh+\frac{1}{2}\rho v^{2}=constant

P\rightarrow Pressure \: energy

\rho gh\rightarrow Potential\: Energy

\frac{1}{2}\rho v^{2}\rightarrow Kinetic \: Energy

 

 

 P_{1}+\frac{1}{2} \rho v_{1}^{2}=P_{2}+\frac{1}{2} \rho v_{2}^{2}

P_{1}-P_{2}=\frac{1}{2} \rho(v_{2}^{2}-v_{1}^{2})=\frac{1}{2}\times 1.2 \times (40^{2}-0)=960\ N/m^{2}

Force acting on the roof 

F=(P_{1}-P_{2})A=960 \times 250=2.4 \times 10^{5}N

Since pressure inside the roof is more than outside so the force will be upward.

Correct option is 1.

 


Option 1)

2.4 x 105 N, upwards

Correct

Option 2)

2.4 x 105 N, downwards

Incorrect

Option 3)

4.8 x 105 N, downwards

Incorrect

Option 4)

4.8 x 105 N, upwards

Incorrect

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