What is the minimum force needed for a syringe to deliver serum into a patient?

[RafaFutbol]

Homework Statement

I'll just post the question given:

You are at the clinic getting your flu shot. The syringe that is being used to deliver the
vaccine has a volume of 2.0 mL, an inner diameter of 6.0 mm, and the needle has an inner
diameter of 0.25 mm. The plunger on which the nurse has placed her finger has a diameter
of 1.2 cm.
(a) What is the minimum force that the nurse needs to apply for serum to enter you?
Take into consideration that you are a little stressed by the whole needle business so
your blood pressure is a bit high: 140-over-100 (be sure you know exactly what those
numbers mean before trying to use them in a calculation!)

(b) The nurse empties the needle in 2 seconds. What is the flow speed of the serum through
the needle?I'm not sure exactly how to get this problem. I know you have to look into the conservation, but what variables would represent what, and what equations could be used to relate all the terms?
I'm really stuck here, any help is appreciated!

 

[horatio89]

a) The first part is on Pascal's Principle. We know that the pressure exerted by the nurse must be equal to the pressure required to push the serum into the blood. (Hint: Do check out what 140 - 100 means, it's very important)

b) Fluid flow rate must always be...?

 

[RafaFutbol]

Ok, for part A I converted it into Pascals
120mm* (1 atm)/760mm*(101.3 kPa)/1atm*(1000 Pa)/(1 kPa)=15994.7 Pa

and found the Force to be:

p=F/A
F=pA
F=pπr^2
F=(15994.7 )π〖(0.003)〗^2
F=0.452 N

but for part b, what variables would I use? Would I use bernoulli's equation of p + 1/2pv^2 + pgy? and the pgy would go away because there would be no change in height.
Am I right for this, or am I off?

*edit: I must be off, because I'm not even using time... how would I include time in this relation, since i don't have the length of the syringe?

 

[horatio89]

fluid flow rate, or dV/dt, which is a product of the velocity and the area, must always be constant for any non-viscous fluid.

 

[RafaFutbol]

So I can get it by calculating:

dV/dt = flow speed
2.0mL/2s = flow speed
flow speed = 1mL/s

is it that easy? :S

 

[horatio89]

dV/dt is rate of volume flow, which is not flow speed (which is in m/s). In a non-viscous fluid, the rate of volume flow must be constant, which is proportional to the flow speed and the area of the flow path.

Hence, dV/dt = A1v1 = A2v2 (V = volume, A= area, v = velocity).

 

[RafaFutbol]

Right, ok.
So, since the syring is 6mm wide:
(1mL/s) / (pi * (3.0mm)^2) = 0.0354 mm/s

are those the proper units to use for the radius?

 

[horatio89]

You're looking for the flow speed in the needle (which differs from the speed in the syringe body), so the diameter should be 0.25mm. Otherwise, it's correct.

 

[RafaFutbol]

Oh ok, I see.
Well thank you so much for the help ^_^
I really appreciate it!

 

[RafaFutbol]

Oh, and just to check... did I do part A correcty?