iAs part of your job in your research you are designing and prototyping a cell infusion system that must deliver cells in culture medium through a syringe as part of a new cell therapy for a large animal study. The cells in solution must be delivered at a constant rate of $1\mathrm{.}2$ mL per second as to not kill the cells by exposing them to excessive shear stress.

a$.$ If you are using an $18$ gauge hypodermic needle to deliver the cell suspension and assuming an incompressible fluid, what is the average velocity $($in cm$/$sec$)$ of the fluid leaving the syringe tip $($also the same at the end of the needle$)?$

b$.$ The internal diameter of the $5$ ml syringe used to deliver the cells is $1\mathrm{.}1$ cm$.$ What plunger velocity $($cm$/$s$)$ is required to maintain this flow rate?

c$.$ You have just used the last $18$ Gauge needle and you have additional trials to complete, and you only have access to a $23$ gauge needle. One of your colleagues starts to deliver the cell suspension at the same flow rate. Remembering your fluid mechanics, you halt the trial saying we need to evaluate this.

i$.$ Perform the calculations that support your decision and state the reason from the standpoint of flow regime classification.

What new volumetric flow rate $($ml$/$s$)$ and plunger velocity $($cm$/$s$)$ must now be used to assure that the cells will not be harmed during delivery?i