Help with problem involving Bernoulli's Equation!?!?!?

Question

A hypodermic syringe contains a medicine with the density of water (Fig. P9.36). The barrel of the syringe has a cross-sectional area of 2.30 multiplied by 10-5 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force, F, of magnitude 2.30 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine's flow speed through the needle. Assume that the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal.

Answer 1

There's not enough information here to get the actual velocity. You'd need to additionally provide either the area of the needle or the flow velocity in the syringe.

What I can tell you is the difference of the squares of the velocities of the flow in the plunger and in the needle. From Bernoulli, the energy density (energy/volume) of pressure is interchangeable with the energy density of velocity. See the ref. There is a height-difference term in his equation which we ignore because the syringe is horizontal.

P2 + ρV2^2/2 = P1 + ρV1^2/2, where ρ is density.

Then V2^2-V1^2 = 2(P1-P2)/ρ

We know P1 - P2 = 1.9/2.1e-5 = 90476 Pa

Thus V2^2-V1^2 = 180952 (m/s)^2.

A fair approximation can be made by assuming the area of the syringe >> the area of the needle. Then V2^2 ~= V2^2-V1^2, so V2 = sqrt(180952) = 425 m/s. But this is off the record; I'll deny everything.