Question

37. The total area of wings of an aeroplane is 10m². The speed of air above and below the wing is 140ms - and
110ms-' Then the force on the aeroplane by air is : low 1.293 109 kg/m3
(a) 48750N
(b) 48000N
(c) 95000N
(d) 50000N​

Answer 1

Answer:

OPTION C :- 48,000 N

★ THIS FORCE IS RESPONSIBLE FOR DYNAMIC LIFT OF AEROPLANE ★

Explanation:

★ FLUID DYNAMICS ★

★ GIVEN ;

» Area of Wing = 10 m²

» Velocity of Air ( above ) wing ( V1 ) = 140 m / s

» Velocity of Air ( below ) wing ( V2 ) = 110 m / s

» Density of air ( d ) = 1.28 Kg / m³

» Atmospheric Pressure = P° ( neglected )

★ » HIEGHT ( h ) = same for both wings so ; [ h2 = h1 ]

★ FORCE ON AEROPLANE ( F ) = ???

______ [ BY USING FORMULA ] _____

★ BERNOULLI'S THEOREM ★

[$P1 + \frac{1}{2} \times d \: \times {v1}^{2} + \: d \times g \times h1 \: = \: P2 \: + \frac{1}{2} \times \: d \: \times {v2}^{2} + \: d \times g \times h2]$

★ P1 - P2 = 1 / 2 × d [ V2² - V1² ] + d ×

g × [ h2 - h1 ]

» P1 - P2 = d / 2 × [ V2² - V1² ] +

( d × g × 0 )

» P1 - P2 = d / 2 × [ ( 140 )² - ( 110 )² ]

» P1 - P2 = d / 2 × [ 19,600 - 12,100 ]

» P1 - P2 = d / 2 × 7500

★ ∆ P = 1.28 / 2 × 7500 ------ ( 1 )

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★ We Know that ;

[ PRESSURE ( ∆ P ) = FORCE ( F ) / AREA ( A ) ]

★ FORCE = PRESSURE × AREA

» F = ∆ P × A

» F = [ 1.28 / 2 × 7500 ] × 10 m²

» F = 4800 × 10

★ FORCE ( F ) = 48,000 NEWTON ★

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ANSWER :- FORCE ON AEROPLANE BY AIR IS ;

[ FORCE ( F ) = 48,000 N ]