Converting Liters to Cubic Inches Using Dimensional Analysis

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SUMMARY

The discussion focuses on converting 1.80 liters (L) of piston displacement to cubic inches using dimensional analysis. The conversion utilizes the facts that 1.00 L equals 1000 cm³ and 1.00 inch equals 2.54 cm. Participants confirm that the last conversion factor must be cubed to maintain unit consistency, resulting in a final volume of approximately 16.8 cubic inches. This method is particularly relevant for automotive enthusiasts calculating engine displacement.

PREREQUISITES
  • Understanding of dimensional analysis
  • Knowledge of unit conversion principles
  • Familiarity with metric and imperial measurement systems
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Learn more about dimensional analysis techniques
  • Explore unit conversion calculators and tools
  • Study the relationship between metric and imperial units
  • Investigate applications of volume calculations in automotive engineering
USEFUL FOR

This discussion is beneficial for automotive engineers, car enthusiasts, and anyone involved in mechanical engineering who requires precise volume conversions for engine specifications.

courtrigrad
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The piston displacement of a car engine is given as 1.80 liters (L). Using only the facts that 1.00L = 1000 cm^3 and 1.00 in. = 2.54 cm, express this volume in cubic inches. So 1.80 L \times (\frac{1000 cm^{3}}{1.00 L})(\frac{1.00 in}{2.54 cm}) [/itex]. Would I have to cube the last term to cancel out the units?<br /> <br /> Thanks
 
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Yes. Cube the whole last proportion- (1.00in./2.54cm)^3. Remember, Your looking for cubic inches as well. There your solving for only inches.
 
Yup. Whenever you convert units to a power, both sides of the convertion must be to the same power.

The answer should end up being aroung 16.8 IIRC, converting CC to cu. in. (I'm a car fanatic, and do these calculations often when figuring muscle car engines)
 

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