Question

What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18L/min$ to $0.48L/\min$ ? The radius of the tap and viscosity of water are $0.5cm$ and $10^{-3}Pas$, respectively. (Density of water: $10^{3}kg/m^3$ )

• A. Unsteady to steady flow
• B. Remains steady flow
• C. Remains turbulent flow
• D. Steady flow to unsteady flow

Answer 1

Answer: (D)

The nature of flow is determined by Reynolds Number.
$R_e=\frac{\rho vD}{\eta }$
$\rho \to$ density of fluid ;
$v\to$ velocity of flow
$D\to$ Diameter of pipe
$\eta \to$ coefficient of viscosity From NCERT
If $R_e<1000\to$ flow is steady
$1000<R_e<2000\to$ flow becomes unsteady
$R_e>2000\to$ flow is turbulent
$R_{\text{einitial }}=10^3\times \frac{0.18\times 10^{-3}}{\pi \times {\left(0.5\times 10^{-2}\right)}^2\times 60}\times \frac{1\times 10^{-2}}{10^{-3}}$
$=382.16$
$R_{\text{efinal }}=10^3\times \frac{0.48\times 10^{-3}}{\pi \times {\left(0.5\times 10^{-2}\right)}^2\times 60}\times \frac{1\times 10^{-2}}{10^{-3}}$
$=1019.09$