Physics of a syringe

By Tue Nguyen

I want to look at how much force the liquid is entering the body with from the tip of the syringe when a nurse injects some drugs into someone’s vein.

I assume that the force applied is 5 N, which is a good estimate of the force applied onto the liquid.
I assume that the radius of the base of the syringe is 0.5cm = 0.005 m. The radius of the needle tip is
0.5mm = 5x10^-4m.

According to Pascal principle, F1/A1=F2/A2 F2=F1*A2/A1= 5*π*(5x10^-4)^2/(π*(5x10^-3)^2)=0.05 N. This is a very small amount of force so it ensures that the liquid coming in does not do any damages to the cells circulating in the blood.