Need help with horizontal syringe Bernoulli's Principle problem.

[b0b10]

Homework Statement

Dr. Jane is ready to inject medicine into Bob. The hypodermic syringe she uses contains a medicine with the same density as water. The barrel of the syringe has a cross-sectional area of 2.50 x 10^-5 m^2. The cross-sectional area of the needle is 1.0 x 10^-8 m^2. In the absence of a force on the plunger, the pressure everywhere is atmospheric pressure. A 2.0 N force is exerted on the plunger, making medicine squirt from the needle to insure there is no air in the needle prior to giving the shot. Determine the speed of the emerging fluid. Assume that the pressure in the needle remains at atmospheric pressure, that the syringe is horizontal, and the speed of the emerging fluid is the same as the speed of the fluid in the needle.

Relevant Equations

(P1) + ρg(y1) + 0.5ρ(v1)^2 = (P2) + ρg(y2) + 0.5ρ(v2)^2
P=F/A
(A1)(v1) = (A2)(v2)

Did I do this problem correctly? I felt like I did this wrong because the answer is suppose to be around 50 m/s.

 

[TSny]

Your work and answer look correct to me.

 

[b0b10]

Your work and answer look correct to me.

Thx