$($From Knight$)$ A syringe has a volume V $,$ an inner diameter of DS$,$ a needle diameter of DN $,$ and a plunger pad diameter $($where you place your finger$)$ of DP $.$ A nurse uses the syringe to inject medicine into a patient whose average blood pressure is Pavg. $($i$)$ What is the minimum average force Favg the nurse needs to apply to the syringe? Favg $=($ii$)$ The nurse empties the syringe in time tinject. What is the flow speed vinject of the medicine through the needle?