Fluids and projectile motion

[Cesare]

Hi, I'm really stuck on this problem and I don't know how to solve it. I have a syringe full of water laid horizontally at a height of 4,9 meters from the ground. I want to calculate the distance that the water coming out of the syringe travels before hitting the ground (it acts like a projectile). A pressure of 100 Pa is applied to the "back" of the syringe (the thing of the syringe that when pushed expels water). The diameter of the back is 1 cm whereas the diameter of the little exit at the front is 2 mm. 

This is my strategy:

• I calculate the areas (by making sure to convert cm and mm to meters) and apply the continuity equation A₁v₁ = A₂v₂ so that I can find the ratios between the velocities.
• I then use Bernoulli's equation to find the final velocity of the water getting out of the syringe.
• Then I use one of the kinematics equations to find the distance travelled by the water using the final velocity of the syringe as the initial velocity of the projectile motion.

The problem is that I cannot find the final pressure in the Bernoulli's equation. What I mean by that is that I have this:

P₁ + 1/2ρv₁² + ρgy₁ = P₂ + 1/2 ρv₂²+ ρgy₂

• ρgy₁ and ρgy₂ cancel out
• To find v₂ I need the final pressure P₂ but I don't have it. How can I find it?

Thanks! I appreciate any help that comes my way.

[FizziksGuy]

I would think the final pressure would be atmospheric...  🙂

[Cesare]

Thanks Dan, wishing you & your family a great Christmas

[FizziksGuy]

All the best to you and yours as well!  Merry Christmas!