A hypodermic syringe is attached to a needle that has an internal radius of 0.30

Question

A hypodermic syringe is attached to a needle that has an internal radius of 0.305 mm and a length of 2.26 cm. The needle is filled with a solution of viscosity 1.88 x 10^-3 Pa.s; it is injected into a vein at a gauge pressure of 15.6 mm Hg. Neglect the extra pressure required to accelerate the fluid from the syringe into the entrance of the needle.

What must the pressure of the fluid of the syringe be in order to inject the solution at a rate of 0.215 mL/s in Pa?

What force must be applied to the plunger, which has an area of 1.80 cm^2

Explanation / Answer

(a) Acc. to  Poiseuille equation is volumetric flow rate : dV / dt = R4 P/ 8 n L where : R is the internal radius of the tube (meters) = 0.305mm= 0.305x10-3m
        volume flow rate : dV /dt =  0.215 mL/s             thus, 0.215 x10-6 = (3.14)(0.305x10-3)4 ( 2079.8 - P2) /8 (1.88 x 10^-3)(0.0226)                0.215x10-6   =  [56.51 - 0.0271 P2]10-9 / 0.339                    72.8 = 56.51 - 0.0271 P2                      P2 = 601.1 Pa (b)     Let,   F be the    force must be applied to the plunger,    which has an area of : A = 1.80 cm^2 = 1.80x10-4    but ,presure : P 2 = F / A                              F = P2 A = (601.1)( 1.80x10-4)                                             =0.108 N                        
                       

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