An inventor proposes a novel tap for making tea. It has single nozzle with a diameter of 2 mm that can be used to deliver hot water (viscosity 0.4 mPa s , density \( 950 \mathrm{~kg} / \mathrm{m}^{3} \) ) or cold milk (viscosity 10 mPa s , density \( 1030 \mathrm{~kg} / \mathrm{m}^{3} \) ).
a) The desired flow rate of the water is \( Q \), which can be delivered using pressure \( P \). A lower flow rate of \( Q / 5 \) is required for the milk (in order to achieve the desired precision), which can be achieved by applying pressure \( \alpha P \). Give a rough estimate for \( \alpha \).