10.4 Explain why

(a) To keep a piece of paper horizontal, you should blow over, not under, it

(b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers

(c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection

(d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel

(e) A spinning cricket ball in the air does not follow a parabolic trajectory

 (a) When we blow over the piece of paper, the velocity of air increases. As a result, the pressure on it decreases in accordance with Bernoulli’s theorem whereas the pressure below remains the same (atmospheric pressure). Thus, the paper remains horizontal.

(b) When we try to close a water tap with our fingers, the area of the outlet of the water jet is reduced, so the velocity of water increases according to the equation of continuity av = constant.

(c) For a constant height, Bernoulli’s theorem is expressed as P +1/2 ρ v= Constant
In this equation, the pressure P occurs with a single power whereas the velocity occurs with a square power. Therefore, the velocity has more effective compared to the pressure. It is for this reason that the needle of the syringe controls flow rate better than the thumb pressure exerted by the doctor.

(d) This is because of the principle of conservation of momentum. While the flowing fluid carries forward momentum, the vessel gets a backward momentum.

(e) A spinning cricket ball would have followed a parabolic trajectory has there been no air. But because of air, the Magnus effect takes place. Due to the Magnus effect, the spinning cricket ball deviates from its parabolic trajectory.