A spherical laundry detergent pod, \(2 \mathrm{~cm}\) in diameter, is placed in a washing machine. The cold wash cycle lasts 20 minutes at \(T=300 \mathrm{~K}\). To effectively clean one's clothes, the pod must dissolve within 5 minutes of being introduced to the washer. If the detergent's molecular weight is \(288.4 \mathrm{~g} / \mathrm{mol}\) with a density of \(1005 \mathrm{~kg} / \mathrm{m}^{3}\), what Reynolds number must the washer provide to insure the clothes get clean? The diffusivity of the detergent in water is \(1 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\). You may assume the flow is turbulent so that:

\[S h_{d} \sim 0.6^{*}\left(R e_{d}\right)^{2 / 3} \mathrm{Sc}^{1 / 3} .\]