Explanation Section 1: 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 × 10 3 Pa . 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 Δ P = ( P atm + ρ g h ) − P atm and it is reduced as Δ P = ρ g h . Given info : The density of the solution is 1.0 × 10 3 kg/m 3 , acceleration due to gravity is 9.8 m/s 2 , and the height of the solution is 1.0 m . The formula for the pressure drop is, Δ P = ρ g h ρ is density of the solution. g is acceleration due to gravity. h is height of the solution. Substitute 1.0 × 10 3 kg/m 3 for ρ , 9.8 m/s 2 for g , and 1.0 m for h to find Δ P . Δ P = ( 1.0 × 10 3 kg/m 3 ) ( 9.8 m/s 2 ) ( 1.0 m ) = 9.8 × 10 3 Pa Thus, the pressure difference between the input and output of the needle is 9.8 × 10 3 Pa . Section 2: 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 0.21 mm . 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 Δ P = [ 8 η L ( Δ V / Δ t ) ] / π R 2 and this expression is rearranged for the radius of the needle. Given info : The volume of the solution is 500 cm 3 , time for the flow is 30.0 min , density of the solution is 10 3 kg/m 3 , viscosity of the solution is 1

11th Edition

ISBN: 9781305952300

Author: Raymond A. Serway, Chris Vuille

Publisher: Cengage Learning

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Chapter 9, Problem 59P

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

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Chapter 9, Problem 58P

Chapter 9, Problem 60P

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

Solution Summary: The author explains the pressure difference between the input and output of the needle, and the formula for the resulting pressure drop is Delta P=rho gh

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Chapter 9 Solutions