In a test experiment on a model aeroplane in | vedclass

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Question

Speed of wind on the upper surface of the wing, $V_{1}=70 m / s$ Speed of wind on the lower surface of the wing, $V_{2}=63 m / s$ Area of the wing, $A

Vedclass · Accepted Answer

$1.51 	imes 10^{3} \;N$

Vedclass · Answer

Speed of wind on the upper surface of the wing, $V_{1}=70 m / s$ Speed of wind on the lower surface of the wing, $V_{2}=63 m / s$ Area of the wing, $A=2.5 m ^{2}$ Density of air, $ho=1.3 kg m ^{-3}$

According to Bernoulli's theorem, we have the relation:

$P_{1}+\frac{1}{2} ho V_{1}^{2}=P_{2}+\frac{1}{2} ho V_{2}^{2}$

$P_{2}-P_{1}=\frac{1}{2} ho\left(V_{1}^{2}-V_{2}^{2}ight)$

Where,

$P_{1}=$ 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.

Lift on the wing $=\left(P_{2}-P_{1}ight) A$

$=\frac{1}{2} ho\left(V_{1}^{2}-V_{2}^{2}ight) A$

$=\frac{1}{2} 1.3\left((70)^{2}-(63)^{2}ight) 	imes 2.5$

$=1512.87$

$=1.51 	imes 10^{3} N$

Therefore, the lift on the wing of the aeroplane is $1.51 	imes 10^{3} \;N$.

Column - $\mathrm{I}$	Column - $\mathrm{II}$
$(a)$ Cohesive force	$(i)$ Useful for writing by chalk on blackboard.
$(b)$ Adhesive force	$(ii)$ Useful in soldering.
	$(iii)$Useful for formation of spherical drops of liquid.

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 $70 \;m s ^{-1}$ 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 atr to be $1.3\; kg m ^{-3} .$

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