Dimensional Analysis Flashcards
Describe the characteristic scale.
- Speed on y axis and length on x-axis
- Particle physics and quantum phenomena are at similar speeds but particle is smaller than quantum
- Relativity and mechanics are at similar lengths but relativity is much faster
How do you use dimensions to derive an equation?
Look at the dimensions of each unit and make sure they are equal on both sides.
What is the dimension/unit of length?
L/m
What is the dimension/unit of mass?
M/kg
What is the dimension/unit of time?
T/s
What is the dimension/unit of current?
I/A
What is the dimension/unit of luminous intensity?
C or J/candles
What is the dimension/unit of temperature?
θ/K
How can you use these fundamental quantities?
Can use them to derive the dimensions of all others (e.g. areas dimension is L^2
What is the notation for dimension of something?
Square brackets around it.
What is the number of independent dimensionless groups of variables equal to?
The number of variables minus the number of independent fundamental quantities.
What does Buckinghams Pi theorem state?
That a set of quantites is said to have independent dimensions if none of these quantities can be represented as a product of powers of the remaining dimensions.
How do you find the dimensionless group after finding the number of dimensionless groups for N = 1?
Raising the dimension to an arbitrary exponent (e.g. α, β and γ) and require the result to be dimensionless (e.g. π = T^α * L^β * (LT^-2)^γ - T: α - 2γ = 0 etc)
What are the 3 steps for dimensional analysis?
- Make list of all variables and identify their dimensions
- Buckinghams Theorem
- Raise to exponent
What do you do if there is more than one dimensionless group?
Do the same steps but for two equations.
