# Viscosity-injection problem

## Homework Statement

Question Details:
A hypodermic syringe is attached to a needle that has an internal radius = .300mm and Length=3.00cm
The needle is filled with solution of viscosity= 2.00 x 10^(-3) Pa.S
And injected at a vein with a gauge pressure of 16mm Hg
What must the pressure of the fluid in the syringe be in order to inject the solution at a rate of .250 mL/s?

## Homework Equations

Poisellous equation

## The Attempt at a Solution

I attempted to use Poisellous Law for Viscous flow
this is my setup

delta p =
[(8/pi *delta V/ delta t)/(r4)]*L*Viscosity

and here i should be able to solve for fluid pressure

my gauge pressure us 16mm Hg-do i need to convert it to Pa?

Last edited:

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ideasrule
Homework Helper

Why do you need to "manipulate velocity into the equation"? 0.250 mL/s is the volumetric flow rate, delta-V/delta-t.

thanks!

does anyone how delta p and gauge pressure are related?
i need to find pressure of fluid, and delta p is only unkown variable i have...so i know
i am solving for it, right?

ideasrule
Homework Helper

Well, blood pressure is at 16mm Hg + atmospheric pressure and you just found delta-P, so just add them together and you'll get the pressure in the needle.

ok im not getting the answer which is suppose to be 6850 Pa.
anyone able to help me out here??

ideasrule
Homework Helper

It looks like the question is looking for the gauge pressure inside the syringe, not total pressure.

yes it is-so how would i approach the problem?

ideasrule
Homework Helper

You know the pressure inside the blood vessel and you know delta-P, the difference in pressure. It's very easy to get the answer from those two values.