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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids3 Marks
Question
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70m s^{–1}$ and $63m s^{-1}$ respectively. What is the lift on the wing if its area is $2.5m^2$? Take the density of air to be $1.3kg m^{–3}$.
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Answer

Speed of wind on the upper surface of the wing, $\mathrm{V}_1=70 \mathrm{~m} / \mathrm{s}$ Speed of wind on the lower surface of the wing, $\mathrm{V}_2=$ $63 \mathrm{~m} / \mathrm{s}$ Area of the wing, $\mathrm{A}=2.5 \mathrm{~m}^2$ Density of air, $\rho=1.3 \mathrm{~kg} \mathrm{~m}^{-3}$ According to Bernoulli's theorem, we have the relation: $\mathrm{p}_1+\frac{1}{2} \rho \mathrm{~V}_1^2=\mathrm{P}_2+\frac{1}{2} \rho \mathrm{~V}_2^2 \mathrm{P}_2-\mathrm{P}_1=\frac{1}{2} \rho\left(\mathrm{~V}_1^2-\mathrm{V}_2^2\right)$ Where, $\mathrm{P}_1=$ Pressure on the upper surface of the wing. $P_2=$ Pressure on the lower surface of the wing. The pressure difference between the upper and lower surfaces of the wing provides lift to the aeroplane.

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