Posted by greg on Wednesday, March 28, 2012 at 10:29pm.
The gauge pressure in the barrel of the syringe is
1.91N/2.44*10^-5 m^2 = 7.83*10^4 Pa
The gauge pressure at the opening of the needle is 0. (1.00 atm absolute)
Use the Bernoulli equation for the velocity at the needle exit.
deltaP(gauge) = 7.83*10^4 N/m^2
= (1/2)(rho)*V^2
rho is the medicine density, 1000 kg/m^3
Solve for V.
V = 12.5 m/s
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