Q4. Beyond the NCERT text: taking the critical Reynolds number for a pipe as 2000, find the critical speed for water (η = 1.0 × 10 Pa s, ρ = 1000 kg m) in a pipe of diameter 2.0 cm.
vc = Re × η/(ρd) = 2000 × 1.0 × 10/(1000 × 0.020) = 0.10 m/s. Above this approximate threshold transition can begin. At 0.15 m/s (Re = 3000) the flow is in a transitional range, so turbulence is not guaranteed.
Q5. Beyond the NCERT text: blood (density 1060 kg m, viscosity about 3.5 × 10 Pa s) flows at 0.30 m/s in an aorta of diameter 2.0 cm. Find the Reynolds number. Is the flow likely to be laminar?
Re = ρvd/η = 1060 × 0.30 × 0.020/(3.5 × 10), about 1820. A steady straight-pipe model would suggest laminar flow. An aorta is pulsatile and flexible, so this number alone does not establish its flow regime.
Q6. Using the hose of Example 1 (about 18.8 L per minute), how long does it take to fill a 0.50 m tank?
0.50 m = 500 L, so the time is 500/18.8, about 27 minutes.