Calculating Fluid Pressure for Viscosity-Injection Problem

[afg_91320]

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?

Answer = 6850 Pa

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?

 

[ideasrule]

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

 

[afg_91320]

oh wow...my bad...never mind -_-

thanks!

 

[afg_91320]

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]

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.

 

[afg_91320]

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

 

[ideasrule]

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

 

[afg_91320]

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

 

[ideasrule]

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.