A) \[1.127\times {{10}^{4}}N\]
B) \[5.0\times {{10}^{4}}N\]
C) \[1.127\times {{10}^{5}}N\]
D) \[3.127\times {{10}^{4}}N\]
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. \[(1/2)\rho {{v}_{1}}^{2}+\rho g{{h}_{1}}+{{P}_{1}}\] \[=(1/2)\rho {{v}_{2}}^{2}\rho g{{h}_{2}}+{{P}_{2}}\]. 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\[=F=(\Delta P)A\] \[\Rightarrow \,\,\,F=1/2\rho A{{v}^{2}}\] where\[=\rho \] density of air\[=1.3kg/{{m}^{3}}\] \[A=20{{m}^{2}},v=29.44m/\sec \]. \[\Rightarrow \,\,F=\{1/2\times 1.3\times 20\times {{(29.44)}^{2}}\}N\] \[=1.127\times {{10}^{4}}N\].
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