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In a test experiment on a model aeropla...

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 `70ms^(-1)and63ms^(-1)` respectively . What is the lift on the wing if its area is `2.5m^(2)` ? Take the density of air to be `1.3kgm^(-3)`.

Text Solution

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Let `v_(1),v_(2)` be the speeds on the upper and lower surface of the wing of aeroplane and `P_(1)andP_(2)` is the pressure on upper and lower surface of the wing respectively and height from ground are `y_(1)andy_(2)` respectively.
`thereforev_(1)=70ms^(-1),v_(2)=63ms^(-1)`,
`y_(1)=y_(2),rho=1.3kgm^(-3)`
From Bernoulli.s equation,
`P_(1)+(1)/(2)rhov_(1)^(2)+rhogh_(1)=P_(2)+(1)/(2)rhov_(2)^(2)+rhogh_(2)`
`thereforeP_(1)-P_(1)=(1)/(2)rho(v_(1)^(2)-v_(2)^(2)) " " [becauseh_(1)=h_(2)]`
`therefore` Upward froce on wings,
`F=(P_(2)-P_(1))A`
`thereforeF=(1)/(2)rho(v_(1)^(2)-v_(2)^(2))A`
`=(1)/(2)xx1.3xx[70^(2)-63^(2)]xx2.5`
`=(1)/(2)xx1.3xx[4900-3969]xx2.5`
`=(1.3)/(2)xx931xx2.5`
`=1512.9N`
`=1.513xx10^(3)N`
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In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surface of the wing are 70 ms^-1 and 63 ms^-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 .

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