Examples of units with non-integer exponents

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SUMMARY

Units with non-integer exponents frequently appear in various scientific fields, particularly in electronics and chemical kinetics. Examples include noise voltage density, expressed in volts per hertz to the power of one-half (V/Hz1/2), and the statcoulomb, which has units of cm3/2·g1/2/s. In chemical kinetics, non-integer exponents arise in rate equations, influencing the units of other factors. Additionally, parameters such as the endurance of an airplane are calculated using lift coefficient to the power of three-halves divided by drag coefficient.

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  • Understanding of dimensional analysis
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  • Knowledge of chemical kinetics and rate equations
  • Basic principles of aerodynamics, specifically lift and drag coefficients
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Scientists, engineers, and students in physics and chemistry who are interested in advanced unit analysis and applications of non-integer exponents in various equations.

Chetlin
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Hi everyone,

Would anyone be able to give me a few examples of places where units with non-integer exponents come up? I know of a couple right now: noise voltage density (?) in electronics has units \text{V}/\text{Hz}^\frac{1}{2} and the statcoulomb has equivalent units \text{cm}^\frac{3}{2}\cdot\text{g}^\frac{1}{2}/\text{s}.

Are there many other places? One answer here on Stack Overflow says that they are "quite common" but I can't think of any other places where they come up.

Thanks!
 
Physics news on Phys.org
When writing the rate equations in chemical kinetics problems we often see non integer exponents for the concentrations. This leads to some interesting units for other factors in the equations.
 
The endurance parameter for an airplane is lift coefficient^3/2 divided by drag coefficient.
Cube loading is weight divided by wing area^3/2.
 

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