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

• A. $1.127\times 10^{4}N$
• B. $5.0\times 10^{4}N$
• C. $1.127\times 10^{5}N$
• D. $3.127\times 10^{4}N$

Answer 1

Answer: (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 $v_2=v_1$
$P_1=P_2+1/2\rho v^2$
$\Rightarrow P_1-P_2=\Delta P=1/2\rho v^2\text{. }$
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 $=1.3kg/m^3$
$A=20m^2,v=29.44m/sec.$
$\Rightarrow F=\left\{1/2\times 1.3\times 20\times (29.44{)}^2\right\}N$
$=1.127\times 10^{4}N.$