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PART - 2 CH - 9 Mechanical Properties of Fluids — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 9 Mechanical Properties of Fluids4 Marks
Question
In a testing experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70 m s ^{-1}$ and 63 m $s^{-1}$ respectively. What is the lift on the wing if its area is $2.5 m^2$ ? Take the density of air to be $1.3 kg m ^{-3}$.
✓

Answer

Suppose the speed of air on the upper and lower surfaces of the wings is $v_1$ and $v_2$ respectively and the air pressure on the upper and lower surfaces is $P_1$ and $P_2$, then
$v_1=70 m / s _2=63 m / s$
and $\quad \rho=1.3 kg / m ^3$
From Bernoulli's principle
$
\begin{aligned}
\frac{P_1}{\rho}+g h+\frac{1}{2} v_1^2 & =\frac{P_2}{\rho}+g h+\frac{1}{2} v_2^2 \\
\frac{P_1}{\rho}-\frac{P_2}{\rho} & =\frac{1}{2}\left(v_1^2-v_2^2\right) \\
P_2-P_1 & =\frac{1}{2} \rho\left(v_1^2-v_2^2\right) \\
& =\frac{1}{2} \times 1.3 \times\left[(70)^2-(63)^2\right] \\
& =\frac{1}{2} \times 1.3 \times[4900-3969] \\
& =\frac{1}{2} \times 1.3 \times 0.931=\frac{1210.3}{2} \\
& =605.15 Pa
\end{aligned}
$
Weight of aeroplane $=$ Pressure difference $\times$ area of wings
$\begin{array}{l}=605.15 \times(2.5) \\ =1.51 \times 10^3 N\end{array}$

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