Uncertainty in Fluid Viscosity Measurement: Improving Result Presentation

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SUMMARY

The discussion focuses on improving the presentation of fluid viscosity measurement results, specifically for water, using the equation governing flow rate through a horizontal pipe. The student calculated viscosity (ƞ) but failed to adequately express the associated uncertainties in measurements of pressure (p), length (l), and radius (r). The instructor emphasized the importance of presenting results with appropriate uncertainty to enhance clarity and accuracy in scientific reporting.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly flow rate equations.
  • Familiarity with viscosity measurement techniques and their significance.
  • Knowledge of uncertainty analysis in experimental physics.
  • Basic skills in mathematical expressions and unit conversions.
NEXT STEPS
  • Research methods for calculating and presenting uncertainty in measurements.
  • Explore advanced fluid dynamics concepts, including laminar vs. turbulent flow.
  • Learn about statistical analysis techniques for experimental data validation.
  • Investigate software tools for fluid viscosity calculations and uncertainty propagation.
USEFUL FOR

This discussion is beneficial for physics students, laboratory technicians, and researchers involved in fluid dynamics and experimental measurement, particularly those focused on enhancing the accuracy and clarity of scientific results.

Diana Moceiparisi
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Homework Statement


a) The equation governing the flow rate,
upload_2017-2-8_18-33-16.png
, of a fluid under streamline conditions through a horizontal pipe of length l and radius r is:

upload_2017-2-8_18-33-34.png


where p is the pressure difference across the pipe and ƞ is the viscosity of the fluid.

Thus, a student conducted an experiment in order to determine the value of ƞ of water and finally states his result as
upload_2017-2-8_18-33-54.png
and estimates the percentage uncertainties in his measurement of
upload_2017-2-8_18-34-13.png
, p, l, and r as
upload_2017-2-8_18-34-41.png
,
upload_2017-2-8_18-35-54.png
,
upload_2017-2-8_18-35-0.png
,and
upload_2017-2-8_18-35-29.png
respectively.

According to the instructor, although his arithmetic and the unit are correct, his statement is unsatisfactory. Thus, in order to improve the result presentation you are required to express his result with appropriate uncertainty.

Homework Equations

The Attempt at a Solution

 

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The "attempt at solution" image you uploaded appears only to say ##\frac{dv}{dt}##.
 
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