If water flows through a pipe of diameter 18cm, and over time the diameter decreases to a diameter of .9cm and at the same time thr viscocity increases by a factor of 1.4. By what factor does the pressure gradiant need to change to stay at a constant volume flow?

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter14: Fluid Mechanics
Section: Chapter Questions
Problem 98P: An oil gusher shoots crude 25.0 m the through a pipe with a 0.100-m diameter. Neglecting resistance...
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If water flows through a pipe of diameter 18cm, and over time the diameter decreases to a diameter of .9cm and at the same time thr viscocity increases by a factor of 1.4. By what factor does the pressure gradiant need to change to stay at a constant volume flow?
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Step 1

Poiseuille’s law is given as: Q=P2-P1πr48ηl

where Q is volume flow rate; (P2-P1) is Pressure Gradient; r is radius; η is viscosity; l is the length 

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