Q.
Air flows horizontally with a speed v=106km/hr. A house has plane roof of area A=20m2. The magnitude of aerodynamic lift of the roof is
1202
154
Mechanical Properties of Fluids
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Solution:
Air flows just above the roof and there is no air flow just below the roof inside the room.
Therefore v1=0 and v2=v.
Applying Bernaulli's theorem at the points inside and outside the roof, we obtain. (1/2)ρv12+ρgh1+P1=(1/2)ρv22+ρgh2+P2.
Since h1=h2=h,v1=0 and v2=v1 P1=P2+1/2ρv2 ⇒P1−P2=ΔP=1/2ρv2.
Since the area of the roof is A, the aerodynamic lift exerted on it =F=(ΔP)A ⇒F=1/2ρAv2
where ρ= density of air =1.3kg/m3 A=20m2,v=29.44m/sec. ⇒F={1/2×1.3×20×(29.44)2}N =1.127×104N.