Fluid Mechanics Viscosity Question 279
Question: Air flows horizontally with a speed$ v=106km/hr $ A house has plane roof of area$ A=20m^{2} $ . The magnitude of aerodynamic lift of the roof is
Options:
A) $ 1.127\times 10^{4}N $
B) $ 5.0\times 10^{4}N $
C) $ 1.127\times 10^{5}N $
D) $ 3.127\times 10^{4}N $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Air flows just above the roof and there is no air flow just below the roof inside the room. Therefore$ V_{1}=0 $ and$ v_{2}=v $ . Applying Bernaulli’s theorem at the points inside and outside the roof, we obtain. $ (1/2)\rho v_{1}^{2}+\rho gh_{1}+P_{1} $ $ =(1/2)\rho v_{2}^{2}\rho gh_{2}+P_{2} $ . Since $ h_{1}=h_{2}=h,,v_{1}=0 $ and $ v_{2}=v_{1} $ $ P_{1}=P_{2}+1/2\rho v^{2}\Rightarrow P_{1}-P_{2}=\Delta P=1/2\rho v^{2} $ . Since the area of the roof is A, the aerodynamic lift exerted on it$ =F=(\Delta P)A $ $ \Rightarrow ,,,F=1/2\rho Av^{2} $ where$ =\rho $ density of air$ =1.3kg/m^{3} $ $ A=20m^{2},v=29.44m/\sec $ . $ \Rightarrow ,,F={1/2\times 1.3\times 20\times {{(29.44)}^{2}}}N $ $ =1.127\times 10^{4}N $ .
BETA
