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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

What radius needle should be used to inject a volume of 500. cm3 of absolution into a patient in 30.0 min? Assume the length of the needle is 2.5 cm and the solution is elevated 1.0 m above the point of injection. Further, assume the viscosity and density of the solution are those of pure water, and that the pressure inside the vein is atmospheric.

To determine
The radius of the needle should be used to inject a volume of a solution into patient.

Explanation

Section1:

To determine: The pressure difference between the input and output of the needle.

Answer: The pressure difference between the input and output of the needle is 9.8×103Pa .

Explanation: As the solution is elevated above the needle, the pressure difference between the input and out of the needle hence atmospheric pressure in the vein is ΔP=(Patm+ρgh)Patm and it is reduced as ΔP=ρgh .

Given info: The density of the solution is 1.0×103kg/m3 , acceleration due to gravity is 9.8m/s2 , and the height of the solution is 1.0m .

The formula for the pressure drop is,

ΔP=ρgh

  • ρ is density of the solution.
  • g is acceleration due to gravity.
  • h is height of the solution.

Substitute 1.0×103kg/m3 for ρ , 9.8m/s2 for g , and 1.0m for h to find ΔP .

ΔP=(1.0×103kg/m3)(9.8m/s2)(1.0m)=9.8×103Pa

Thus, the pressure difference between the input and output of the needle is 9.8×103Pa .

Section2:

To determine: The radius of the needle should be used to inject a volume of a solution into patient.

Answer: The radius of the needle should be used to inject a volume of a solution into patient is 0.21mm .

Explanation: According to the principle of Poiseuille, the pressure difference required producing volume flow rate of the given fluid with viscosity η through a needle of radius R and length L is ΔP=[8ηL(ΔV/Δt)]/πR2 and this expression is rearranged for the radius of the needle.

Given info: The volume of the solution is 500cm3 , time for the flow is 30.0min , density of the solution is 103kg/m3 , viscosity of the solution is 1

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