The lift on a spinning circular cylinder in a freestream with a velocity of 10 m/s is measured as $ L_1 $ at standard sea level conditions and $ L_2 $ at an altitude of 10,000 ft. Assume that both cases generate the same circulation around the cylinder.

How do you compare $ L_1 $ and $ L_2 $?

Please choose one of the following alternatives:
(i) $ L_1 = L_2 $
(ii) $ L_1 > L_2 $
(iii) $ L_1 < L_2 $
(iv) None of them

When a spinning circular cylinder is placed in a freestream, it generates lift due to the circulation around the cylinder. The lift force is influenced by various factors, including the velocity of the freestream and the altitude at which the measurements are taken.

In this case, the lift force on the cylinder is measured as L1 at standard sea level conditions and L2 at an altitude of 10,000ft. As the altitude increases, the air density decreases. Since the lift force is directly proportional to the air density, we can expect a change in the lift force between L1 and L2.

At higher altitudes, the air density is lower compared to standard sea level conditions. This decrease in air density results in a decrease in the lift force on the cylinder. Therefore, we can conclude that L1 is greater than L2.

Therefore, the correct answer is (ii) L1 > L2.

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