Rayleigh Dimensional Method
Rayleigh's method assumes Q = k x^a y^b ... with dimensionless k, substitutes dimensional formulas, and equates independent base exponents to solve the unknown powers, provided the stated variables form a sufficient independent set.
Why this shows up in the exam
Estimating pendulum periods · Scaling fluid or wave relations · Building similarity laws
Learn the idea
A power-law dependence can be inferred by matching base-dimension exponents. If a quantity depends only on listed variables, assign unknown powers, then let each base dimension vote on those powers through simultaneous equations.
🧠 Memory hook: Unknown powers become linear equations in dimensional exponents.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Q = k xᵃ yᵇ zᶜ — assumed monomial dependence
- [Q] = [x]ᵃ [y]ᵇ [z]ᶜ — dimension equation used to solve exponents
How to approach it
- 1List only stated governing variables
- 2Assume a product of powers
- 3Match each base exponent and solve
Common slip-ups that cost marks
- •Including a dimensionful proportionality constant silently
- •Using dependent variables as if independent
- •Claiming the dimensionless numerical constant is determined
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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