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~christina~

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**[SOLVED] Needle and pressure (Bernoulli's equation?)**

## Homework Statement

A hypodermic syringe contains medicine having the density of water. Barrel has cross sectional area A= 2.50x10^-5 m^2 and the needle has a cross sectional area a= 1.00x10^-8 m^2. IN the absence of a force on the plunger the pressure everywhere is 1 atm.

A force of magnitude 2.00N acts on the plunger making medicine squirt from the needle. Determine the speed of the medicine as it leaves the needle's tip.

http://img123.imageshack.us/img123/1442/66319119wa1.th.jpg

## Homework Equations

A1v1= A2v2

[tex] P_1 + 1/2 \rho v^2 + \rho gy_1 = P_2 + 1/2\rho v^2 + \rho g y_2 [/tex]

P= F/A

## The Attempt at a Solution

I'm not sure how to get started but I'm thinking that if the plunger is pushed with a force of 20N then

[tex]P_1= 20.0N/ 2.50x10^-5m^2 [/tex]

[tex] P_1= 8e5 Pa [/tex]

I was then thinking of plugging that into the Bernoulli's equation b/c it relates pressure however...I'm confused again...

using the bernoulli's equation... noting that no change in height

[tex]P_1 + 1/2 \rho v_1^2 = P_2 + 1/2 \rho v_2^2 [/tex]

[tex]v_1= (A_2/A_1) *v_2 [/tex] =>

**no v1 or v2**...

**I'm basically not sure since I do not have v1 or v2 but I do have P1...**

P2 is different as is v2. v1 I was initially thinking it was at rest but then I thought it could not be since the plunger moved with force of 20N

Now I'm starting to think it relates to :

P2 is different as is v2. v1 I was initially thinking it was at rest but then I thought it could not be since the plunger moved with force of 20N

Now I'm starting to think it relates to :

[tex]\Sum F= F_{plunger} - Fatm= ma [/tex] => (where I can say P=F/A) but how can I do that if I don't have the m and not to mention I have no t or x so I wouldn't be able to use a as acceleration anyhow

I really would appreciate it if someone could help me out (especially with how to apply F to the equations to solve for v2)

Thanks alot

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