Physics: Attempted below but wrong!! where? please help explain thanks!!!?

[Happy]

the ANSWER I TRIED BELOW IS WRONG IT SAYS “Your response differs from the correct answer by orders of magnitude.” WHAT DOES THAT MEAN? PLEASE HELP TELL ME WHERE DID I GO WRONG ABOUT. THANKS SO MUCH!!!!


A hypodermic syringe contains a medicine with the density of water. The barrel of the syringe has a cross-sectional area A = 2.60 10-5 m2, and the needle has a cross-sectional area a = 1.00 multiplied by 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1 atm. A force F of magnitude 3.00 N acts on the plunger, making the medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip.

P = 3/(2.6e-5) = 115384.62 N/m^2.

V1*a = Vo*A, so:
V1 = (A/a)*Vo = (2.6e-5/e-8) = 2600

Pressure + density*v^2/2
= (Po +115384.62) + 1000*Vo^2/2 = Po + 1000*V1^2/2
= Po + 1000*(A/a)^2*Vo^2/2

115384.62 + 1000*Vo^2/2 = 1000*(A/a)^2*Vo^2/2
115384.62 = 500*Vo^2 ((A/a)^2 - 1)
= 500*((2600)^2 - 1)*Vo^2
= 500*(2.6^2) *e8 - 1)*Vo^2
~5*(2.6)^2*e8*Vo^2

So:
Vo^2 = (115384.62/(5*2.6^2))e-8
= 3.4E-5
and so:
Vo = 5.06e-3 (m/s)
and
V1 = (A/a)*Vo
= (2600)* 3.4E-5
= 0.089 m/s