JEE PYQ: Mechanical Properties Of Fluids Question 2
Question 2 - 2021 (16 Mar 2021 Shift 2)
What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and $10^{-3}$ Pa s, respectively. (Density of water: $10^3$ kg/m$^3$)
(1) Unsteady to steady flow
(2) Remains steady flow
(3) Remains turbulent flow
(4) Steady flow to unsteady flow
Show Answer
Answer: (4) Steady flow to unsteady flow
Solution
The nature of flow is determined by Reynolds Number. $R_e = \frac{\rho v D}{\eta}$ If $R_e < 1000 \to$ flow is steady $1000 < R_e < 2000 \to$ flow becomes unsteady $R_e > 2000 \to$ flow is turbulent $R_{e,\text{initial}} = 10^3 \times \frac{0.18 \times 10^{-3}}{\pi \times (0.5 \times 10^{-2})^2 \times 60} \times \frac{1 \times 10^{-2}}{10^{-3}} = 382.16$ $R_{e,\text{final}} = 10^3 \times \frac{0.48 \times 10^{-3}}{\pi \times (0.5 \times 10^{-2})^2 \times 60} \times \frac{1 \times 10^{-2}}{10^{-3}} = 1019.09$ Flow changes from steady to unsteady.
BETA
