Air streams horizontally past an air plane. The speed over the top surface is 60m/s and that under the bottom surface is 45m/s. The density of air being 1.293kg/m3, calculate the difference in pressure across the wing.
A
1018N/m2
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B
516N/m2
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C
1140N/m2
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D
2250N/m2
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Solution
The correct option is A1018N/m2 Applying the bernoulli's equation for two points 1 and 2, just above the wing (top surface) and just below the wing (bottom surface ) of the aircraft. (∵ wings of aircraft play role in aerodynamics or lifting of plane)
v1=60m/s (speed of air at top surface) v2=45m/s (speed of air at bottom surface) (v1>v2), therefore (P2>P1) from Bernoulli's principle of energy conservation. ⇒P1+ρgh+12ρv21=P2+ρgh+12ρv22 ⇒P2−P1=12ρ(v21−v22)
or ΔP=12×1.293×((60)2−(45)2) ∴ΔP=1018.23≈1018N/m2