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 air does not follow a parabolic trajectory
When we blow over the paper, the air above moves faster. According to Bernoulli's principle, faster moving air has lower pressure. The pressure above the paper decreases while pressure below remains atmospheric. This pressure difference creates an upward lift, keeping the paper horizontal. Blowing under would decrease pressure below, causing the paper to fall.
When fingers partially close the tap opening, the cross-sectional area decreases. According to conservation of mass and the continuity principle, to maintain the same flow rate, velocity must increase as area decreases. Hence, water gushes out as fast jets through the small openings between fingers.
The flow rate through a needle depends significantly on its cross-sectional area. According to fluid flow principles, the flow rate is more sensitive to changes in the needle's dimensions than to variations in thumb pressure. A fixed needle size ensures consistent flow rate, making it a better control mechanism than variable thumb pressure.
When fluid flows out of a small hole in a vessel, it carries momentum in the forward direction. By conservation of momentum, the vessel must experience an equal and opposite momentum, resulting in a backward thrust on the vessel.
When a cricket ball spins in air, air moves faster on one side relative to the other due to the spin. According to Bernoulli's principle, this creates a pressure difference across the ball. The pressure difference causes a lateral force, making the ball deviate from its parabolic trajectory.
Explanation
This question tests understanding of Bernoulli's principle, conservation of mass/continuity equation, and conservation of momentum in fluid mechanics. The context mentions Bernoulli's principle and conservation of mass in relation to fluid flow speed at constrictions (9.3d). Each phenomenon can be explained using these fundamental principles from the chapter.