thermo - dimen anal

concept - dimension

a measure of physical quantity without numerical values (e.g mass, length,time)

concept - unit

a way to assign a numerical value to a specific dimension

how many primary dimensions are there

7

which primary dimension is represented by the symbol m

mass

what is the primary dimension symbol for electric current

I

the primary dimension ‘ amount of light’ uses which symbol

C

what is the primary dimension symbol for ‘amount of matter’

N

SI unit for the primary dimension of temperature (T)

Kelvin (K)

English unit for the primary dimension of temperature (T)

Rankine (R)

Name the English unit used for the primary dimension of mass

Pound-mass (lbm)

besides T, what greek letter is sometimes used as a symbol for temperature

Theta

state the base dimensions for acceleration

Lt^(-2)

State the base dimensions for force F

mLt^(-2)

state the base dimensions for density (ρ).

mL^(-3)

State the base dimensions for Pressure (P).

mL^(-1)t^(-2)

The dimensions of stress are identical to the dimensions of _____.

pressure

State the base dimensions for Energy.

mL²t^(-2)

State the base dimensions for Power.

mL² t^(-3)

State the base dimensions for Torque.

mL²t^(-2)

State the base dimensions for Specific Heat (c).

L²t^(-2)T^(-1)

State the base dimensions for Viscosity (μ).

mL^(-1)t^(-1)

List the three conditions required for complete similarity.

geometric similarity, kinematic similarity, and dynamic similarity

Which type of similarity requires the model and prototype to have the same shape?

geometric similarity

Which type of similarity requires velocities at corresponding points to be proportional?

kinematic similarity

Dynamic similarity is achieved when all _____ scale by a constant factor.

forces

In the Buckingham Pi theorem, what is the formula to calculate k (number of Π groups)?

k= n− j

In the Buckingham Pi theorem, what does the variable n represent?

the total number of parameters in the problem

In the Buckingham Pi theorem, what does the variable j represent?

the number of primary dimensions included in the parameters

Step 4 of the Method of Repeating Variables involves choosing j _____.

repeating parameters

Step 4 of the Method of Repeating Variables involves choosing j _____.

write the final functional relationship and check the algebra

When choosing repeating variables, they must collectively include all _____.

primary dimensions in the problem (e.g M,L,t)

Can a dependent parameter be chosen as a repeating variable?

no

What is the purpose of the Method of Repeating Variables?

To generate non-dimensional parameters (Π groups).