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

\(R _{ e }=\frac{\rho vD }{\eta}\)

\([\rho \rightarrow\) density of fluid ;

\(\eta \rightarrow\) coefficient of ;

\(v \rightarrow\) velocity of flow ;

\(D \rightarrow\) Diameter of pipe\(]\)

From NCERT

If \(R _{ e }<1000 \quad \rightarrow\) flow is steady

\(1000< R _{ e }<2000 \rightarrow\) flow becomes unsteady

\(R _{ e }>2000 \rightarrow\) flow is turbulent

\(R _{ e \text { initial }}=10^{3} \times \frac{0.18 \times 10^{-3}}{\pi \times\left(0.5 \times 10^{-2}\right)^{2} \times 60} \times \frac{1 \times 10^{-2}}{10^{-3}}\)

\(=382.16\)

\(R _{ efinal }=10^{3} \times \frac{0.48 \times 10^{-3}}{\pi \times\left(0.5 \times 10^{-2}\right)^{2} \times 60} \times \frac{1 \times 10^{-2}}{10^{-3}}\)

\(=1019.09\)