Question

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: $10^{3} \,kg / m ^{3}$ )

• 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 \rightarrow $ density of fluid ;
$v \rightarrow $ velocity of flow
$D \rightarrow$ Diameter of pipe
$\eta \rightarrow $ coefficient of viscosity From NCERT
If $R _{ e }<1000 \rightarrow$ flow is steady
$1000< R _{ e }<2000 \rightarrow$ flow becomes unsteady
$R _{ e }>2000 \rightarrow$ 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}} $
$=1019.09$