   Chapter 9, Problem 55P

Chapter
Section
Textbook Problem

A straight horizontal piper with a diameter of 1.0 cm and a length of 50 m carries oil with a coefficient of viscosity of 0.12 N · s/m2. At the output of the pipe, the flow rate is 8.6 × 10−5 m3/s and the pressure is 1.0 atm. Find the gauge pressure at the pipe input.

To determine
The gauge pressure at the pipe input.

Explanation
From Poiseuille’s law, the flow rate at the input of the pipe is flowrate=(P1P2)πR4/8ηL and this expression is rearranged for the gauge pressure.

Given info: The diameter of the pipe is 1.0cm , coefficient of viscosity of oil is 0.12Ns/m2 , flow rate of the oil at the output of the pipe is 8.6×105m3/s , the pressure at the output of the pipe is 1.0atm , and length of the pipe is 50m .

The formula for the gauge pressure at the pipe input is,

P1P2=8ηL(flowrate)πR4

• η is coefficient of viscosity of oil.
• L is length of the pipe.
• R is radius of the pipe.

Substitute 0.12Ns/m2 for η , 50m for L , 8.6×105m3/s for flowrate , 1

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