Question

If air blown through the space between a calendar suspended from a nail on a wall and the wall, then
A) The calendar moves close to the wall
B) The calendar moves farther away from the wall
C) The position of the calendar does not change
D) The position of the calendar may or may not change

Answer 1

Hint
Bernoulli’s theorem links the pressure of the air when the air is stationary and when it is flowing behind the calendar. We can use this relation to determine the pressure behind the calendar when the air is flowing through to determine whether it is moving closer or further away from the wall.

Formula used: In this solution we will be using the following formula,
Bernoulli’s Equation: $ P = {P_{atm}} + \rho gh + \dfrac{1}{2}\rho {v^2} $ where $ P $ is the pressure of the air at a certain point, $ {P_{atm}} $ is the atmospheric pressure, $ h $ is the height of the system, and $ v $ is the velocity of the air.

Complete step by step answer
We’ve been given that a calendar is suspended from a nail on a wall which implies that the calendar is quite close to the wall. Now when we’re blowing no air, the pressure behind the calendar will only be due to the atmospheric pressure. Since the air is stationary at this point, no pressure will be created due to the flow of air either.
Now when air is blown between the calendar and the wall, the velocity of the airflow is \[v\]. As a result, it will increase the pressure behind the calendar because of the term $ \dfrac{1}{2}\rho {v^2} $. To keep the total pressure constant, the ambient pressure behind the calendar will lower from $ {P_{atm}} $. This decrease in the pressure between the wall and calendar causes the calendar to move closer to the wall as the air on the outside of the calendar will move towards the wall to balance the pressure.
So the correct option will be (A).

Note
Here, we have assumed that the space between the calendar and the wall is very small so the atmosphere cannot compensate for the pressure drop due to the flow of air behind the calendar immediately. Also, in a real-life situation, the air slows down as it passes through the calendar, and as a result, one end of the calendar might move closer to the wall but not the other.