Math Wizards I need some help (flow computation)

[OTEP]

I'm trying to compute the water pressure as water comes out of a syringe.

I'm using a standard 10 cc syringe (15.8mm diameter), with a gauge 20 (green cannula .603mm inner diameter) attached to its end.

How can I compute for the water pressure coming out at the end? What formula will I use?

Do I need to time it?

I'm working on a small project. Thank you.

[ghosthunter]

I'm trying to compute the water pressure as water comes out of a syringe.

I'm using a standard 10 cc syringe (15.8mm diameter), with a gauge 20 (green cannula .603mm inner diameter) attached to its end.

How can I compute for the water pressure coming out at the end? What formula will I use?

Do I need to time it?

I'm working on a small project. Thank you.

The pressure is simple.

Just compute the area on the plunger. = A1

Get the area of the output (guage 20). = A2

P1 is the force at the plunger.

P2 is the unknown pressure at guage 20 outlet.

Original equation should be: P1A1 = P2A2

interpolating:

P2 = (P1A1)/A2

Trying to make some sort of auto-intravenous injection device??

[kinyo]

I believe the formula needed is called the Bernoulli's Equation. When the height difference is negligible, e.g. in a syringe, the equation is

P1 + (1/2)(p)(v1^2) = P2 + (1/2)(p)(v2^2)

and the equation of continuity (A1)(v1) = (A2)(v2).

However, while on air, pressure on the water exiting the needle is simply atmospheric pressure! And given that the needle have constant inner diameter throughout its length, flow velocity is the same along its length, so the pressure within the needle is also atmospheric.

The velocity within the syringe is of course different from that on the needle, so the pressure inside the syringe would not be atmospheric and would follow Bernoulli's Equation.

The equations above are usually applied in determining the flow velocities. For example, if you empty the 10cc syringe in 2.0 seconds, you can determine the velocities and the pressure (or force) applied at the plunger.

In the case of injecting medicine on a patient, the pressure on the fluid exiting the needle would be blood pressure.

HTH