Question

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

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

Answer 1

The correct option is C Steady flow to unsteady flow

The nature of flow is determined by Reynold`s number.
$$R_e=\frac{\rho vD}{\eta }$$ If $Re<1000\to$ flow is steady
$1000<R_e<2000\to$ flow becomes unsteady
$R_e>2000\to$ flow is turbulent

$(R_e{)}_{initial}={10}^3\times \frac{0.18\times {10}^{-3}}{\pi \times (0.5\times {10}^{-2}{)}^2\times 60}\times \frac{1\times {10}^{-2}}{{10}^{-3}}=382.16$
$(R_e{)}_{final}={10}^3\times \frac{0.48\times {10}^{-3}}{\pi \times (0.5\times {10}^{-2}{)}^2\times 60}\times \frac{1\times {10}^{-2}}{{10}^{-3}}=1019.09$
So, flow will become steady to unsteady.