Fluid Dynamics: Calculating Speed and Force in Syringe Experiments"

[vincekillics]

Homework Statement

It is time for aged physics lecturers to have their flu shots but even that can be interesting. Assume the density of the vaccine in the syringe is the same as the density of water. The diameter of the syringe is 6mm, the length of the needle is 3cm and by reading the packet that the needle comes in we find out that, the needle has a cross sectional area of 1.00 x 10-8m2. When the full syringe is sitting on the medical tray no vaccine comes out of it, but when the nurse picks it up and applies 2.00N of force on the plunger the vaccine squirts out of the end removing any air bubbles in the liquid.a) With what speed did the medicine leave the tip of the needle during the air bubble removal process if the nurse held the syringe so the needle was pointing directly upward?b) The whole process gives the lecturer an idea for a physics demonstration. By taking a syringe with a diameter of 29.2mm that can hold 50ml of coloured water and connecting it to a long piece of tubing with an internal diameter of 2mm they could push the coloured water from the syringe into the tubing and by lifting the open end of the tube up as high as possible they could test Bernoulli’s principle. So a student was dispatched with the tubing to the top of the physics building (9m high). They dropped one end of the tube down to another student who attached it to the end to the water filled syringe. Then force was applied to the syringe and the water was pushed up through the tubing to the top of the building. In the ideal situation (no friction between the water and the inside walls of the tubing) what force would need to be applied to the syringe to get the water to the top of the building?

Homework Equations

Bernoulli's equation

The Attempt at a Solution

as for a) I used the bernoulli principle P1 + 1/2pv1^2 + pgh1 = P2 + 1/2pv2^2 + pgh2, and reduce it to v2^2 - v1^2 = 2(P1-P2)/p, to calculate P1, I use P=F/A and got 17699.115 Pa, to calculate P2 is the force same as P1?, because of missing v1 and P2, I could not find the v2, and I can't ingnored the potential energy because the syringe holds vertically upwards.
as for b) I have no idea for this

 

[Simon Bridge]

If P1 is the force pressing on the plunger, then P2 is the force pressing on the open end of the needle right? So what, physically, is actually pressing in that end?
Notice that you are also told what happens, or doesn't happen, when the syringe is horizontal with no additional applied force.

 

[haruspex]

as for a) I used the bernoulli principle P1 + 1/2pv1^2 + pgh1 = P2 + 1/2pv2^2 + pgh2, and reduce it to v2^2 - v1^2 = 2(P1-P2)/p, to calculate P1, I use P=F/A and got 17699.115 Pa, to calculate P2 is the force same as P1?, because of missing v1 and P2, I could not find the v2, and I can't ingnored the potential energy because the syringe holds vertically upwards.

P1 and P2 are pressures, not forces.
You are told the nurse exerted a certain force. I would take that as being from the nurse's point of view, so any other forces/pressures present are in addition to this. What else would there be? What is the pressure beyond the tip of the needle?

Before the nurse presses on the plunger, the fluid is at rest, so you can take all KE as being a result of that pressure.

The potential energy is awkward. You are told the length of the needle but not the length of the syringe. The force exerted by the nurse will include supporting the entire column. But since 2N would be enough to support the fluid in a 6m long syringe of that diameter, I think you can safely ignore it.