Lift force on an airplane wing

Classical Mechanics Level 2

The air above an airplane wing travels at 200 m/s 200 \text{ m/s} , while the air below it travels only 180 m/s 180 \text{ m/s} . Find the magnitude of the lift force if the density of air is ρ = 1.29 kg/m 3 \rho = 1.29 \text{ kg/m}^3 and the area of the wing is A = 2 m A = 2\text{ m} .

Assume the height of the wing is negligible.


The answer is 9804.

July Thomas by July Thomas , 30, USA

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1 solution

July Thomas
Apr 13, 2016

Relevant wiki: Bernoulli's Principle (Fluids)

Bernoulli's equation without a height difference is

P 1 + 1 2 ρ v 1 2 = P 2 + 1 2 ρ v 2 2 P_1 + \frac12 \rho v_1^2 = P_2 + \frac12 \rho v_2^2

Solve for the difference in pressure, as this will relate to the net force.

P 1 − P 2 = 1 2 ρ ( v 2 2 − v 1 2 ) P_1 - P_2 = \frac12 \rho(v_2^2 - v_1^2)

P 1 − P 2 = 1 2 ( 1.29 ) ( 20 0 2 − 18 0 2 ) = 4 , 902 Pa P_1 - P_2 = \frac12 (1.29)(200^2 - 180^2) = 4,902 \text{Pa}

From P = F A , P=\frac{F}{A},

F n e t = ( P 1 − P 2 ) A = 4 , 902 ( 2 ) = 9 , 804 N . F_{net} = (P_1-P_2)A = 4,902(2) = 9,804 \text{N}.

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