GS-1 Physical Sciences Question 3

[ozairmh8911]

I don't understand the explanation for this question. What is the relationship between density and altitude? I tried doing this question by using B's equation: P1 + 1/2pv1^2 + pgy1 = constant. But I could not get the answer. And the formula in the question stem does not take altitude into account.

Thanks.

[jellywing_2058]

The explanation says that at the lower altitude the plane will experience a greater lift because of a higher air density; and air density ρ does very much figure in the equation for the lift force. The reason behind the relationship between density and altitude is not the Bernoulli’s equation; it is simply that air composed of all kinds of gases is compressible.

Therefore imagine a cylindrical column of air, extending from the surface of the Earth to the end of the atmosphere. A point at a higher altitude has a shorter column of air that presses down upon it, and therefore the air is under the influence of lesser mass of air. This means a lesser weight of air compresses it. So being more compressed, the air at lower altitudes is denser.

Also the Gravitational force/Gravitational field is stronger because
g = G M/ r^2
where r is the distance from the Center of the Earth, which is lesser at lower altitudes making g larger.

So not only the Quantity of Air is more, but also the Gravitational force is large at the lower altitudes. Both cause the air to be denser at lower altitudes.

[dnpgr16513]

If density is lower at higher altiudes, then why does is the answer GREATER lift? Shouldn't it be less when looking at the equation????????

[jellywing_2058]

The answer is:

[dnpgr16513]

Ok, gotcha. This is what makes me miss stupid questions.

THANKS!