COMEDK · Physics · 11. Mechanical Properties of Fluids

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are \(v_1\) and \(v_2\), respectively. If \(A\) is the cross-sectional area of the wing and \(\rho\) is the density of air, then the upward lift is

A \(\dfrac{1}{2} \rho A\left(v_1+v_2\right)\)
B \(\dfrac{1}{2} \rho A\left(v_1-v_2\right)\)
C \(\dfrac{1}{2} \rho A\left(v_1^2-v_2^2\right)\)
D \(\dfrac{1}{2} \rho A\left(v_1^2+v_2^2\right)\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{1}{2} \rho A\left(v_1^2-v_2^2\right)\)

Step-by-step Solution

Detailed explanation

According to Bernoulli's principle for streamline flow, the pressure \(P\) and velocity \(v\) at any two points on a streamline are related by \(P + \dfrac{1}{2} \rho v^2 = \text{constant}\). Let \(P_1\) and \(P_2\) be the pressures on the upper and lower surfaces of the wing…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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