Solving Pressure of Syringe Homework Statement

[mercury126]

Homework Statement

A 2.0 mL syringe has an inner diameter of 6.0mm, a needle inner diameter of 0.25mm, 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?
b. The nurse empties the syringe in 2.0s. What is the flow speed of the medicine through the needle?

Homework Equations

P = pgh
0.5pv^2 + pgh + P = constant
Av = constant
P = F/A

The Attempt at a Solution

Using P = pgh, I found the minimum pressure required to inject the medicine to be 18659.2 Pa. I tried to plug that into P=F/A but didn't get the right answer. For a, the answer is supposed to be 0.377N and for b, 20.4m/s. Does anyone know how to get these answers? Thanks.

 

[learningphysics]

convert 100mm Hg into Pa...

Then use that in P = F/A, where A is the area of the inner diameter, 6.0mm.

Then use the 0.25mm area to get the flow velocity.

 

[talaroue]

how do you get the flow velocity from the two area's? without any velocities?