A 2.50 mL syringe has an inner diameter of 4.00 mm, a needle inner diameter of 0

Question

A 2.50 mL syringe has an inner diameter of 4.00 mm, a needle inner diameter of 0.210 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100.

a) What is the minimum force the nurse needs to apply to the syringe? (in N's)

b) The nurse empties the syringe in 2.70 s. What is the flow speed of the medicine through the needle? (in m/s)


I've tried to do part a many times and I've gotten these answers (in N's) and none of them are right. I haven't tried to do part b yet.
3.66*10^(-5)
2.59*10^(-5)
.491
.351

Thank you so much for your help!

Explanation / Answer

given

because the patients blood pressure is 140/100 the minimum fluid pressure needs to be 100mm of Hg above atmospheric pressure . since 760mm of Hg is equalent to 1atm = 1.013 * 10 ^5 pa

the miniumum pressure is 100mm = 1.333 * 10 ^4 pa. the excess pressure in the fluid is due to force F pushing on the internal 4.0mm diameter piston the presses against the liquid

thus minimum force the nurse needs to apply to syringe is

diameter of inner syringe d = 4.00mm

radius of syringe   r = d/2

                              = 2.00mm = 0.002m

F = fluid pressure * area of plunger

   = 1.333 * 10 ^ 4 pa * ( 0.0020m)2 = 0.1674N

b) the flow rate Q = v/A

                           v = Q / A

                           v = (2.50x10^-6 m^3 /2.70s ) / ( 0.210x10^-3 m / 2)2   

                           v = 26.74 m/s

                        

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