Chapter 9, Problem 55P

### College Physics

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

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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 Poiseuilleâ€™s law, the flow rate at the input of the pipe is flowâ€‰rate=(P1âˆ’P2)Ï€R4/8Î·L and this expression is rearranged for the gauge pressure.

Given info: The diameter of the pipe is 1.0â€‰cm , coefficient of viscosity of oil is 0.12â€‰Nâ‹…s/m2 , flow rate of the oil at the output of the pipe is 8.6Ã—10âˆ’5â€‰m3/s , the pressure at the output of the pipe is 1.0â€‰atm , and length of the pipe is 50â€‰m .

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

P1âˆ’P2=8Î·L(flowâ€‰rate)Ï€R4

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

Substitute 0.12â€‰Nâ‹…s/m2 for Î· , 50â€‰m for L , 8.6Ã—10âˆ’5â€‰m3/s for flowâ€‰rate , 1

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