A hypodermic syringe contains a medicine with the density of water. The barrel of the syringe has a cross-sectional area of 2.5*10^-5 m^2. In the absense of a force on the plunger, making the medicine squirt from the needle. If the syringe is horizontal and the pressure within the syringe remains 1 atm, what is the medicine's flow speed through the needle?
Pressure = Force/Area
Flow Rate: A1v1=A2v2
P + ρv2/2 + ρgy = constant for a whole pipe
((( ρ (the last two p-looking things) = rho (density) )))
The Attempt at a Solution
I tried dividing the force on the syringe by the area to get a pressure, but I'm not sure how to work with that pressure. And I think you have to use the flow rate equation to calculate the velocity out of the needle, because it looks as if the fluid would have different speeds in different parts of the syringe. However, we're not given a second area... how can we find the speed at the end of the syringe without the second area?
I'm pretty lost.