Q4. Water speeds up from 1.0 m/s to 3.0 m/s as it flows along a horizontal pipe. By how much does its pressure fall? Take the density of water as 1000 kg m.
ΔP = ½ρ(v22 − v12) = ½ × 1000 × (9 − 1) = 4000 Pa.
Q5. Why does Bernoulli’s equation not apply exactly to honey flowing slowly through a narrow tube, or to the white water of a rapid?
Honey is very viscous, so a lot of mechanical energy is lost to internal friction, which the equation ignores. White water is turbulent, so the velocity and pressure at each point keep fluctuating and the flow is not steady.
Q6. Beyond the NCERT text: an open tank stands on the ground with water to a height H. At what height should a small hole be made so that the jet lands farthest from the tank, and how far does it reach?
A hole at height y has depth H − y, so v = √(2g(H − y)), and the jet falls y in a time √(2y/g). The range is 2√((H − y)y). (H − y) and y have a fixed sum H, so their product is largest when they are equal: y = H/2, and then the range equals H. Holes at heights y and H − y give the same range.