5. Dimensions and units, ratios and coefficients Flashcards
What are dimensions?
Basic concepts of physical measurements or what we are measuring.
list some types of dimensions?
- Length (L)
- Mass (M)
- Time (T)
- Temperature (θ)
We can use fundamental dimensions to represent equations. Find forces fundamental dimensions using Newton’s second law, F = ma.
F = ma
F = M x LT^-2
F = MLT^-2
What are some geometric quantities’ fundamental dimensions?
How do we refer to models and prototypes in formulas?
models - small scale, will feature a ‘m’ subscript
prototypes - large scale, will feature a ‘p’ subscript or ‘f’ for full scale
What is some Geometric ratios and why do we use them?
Ratios are dimensionless and allow models and prototypes to be scaled appropriately by these ratios.
- Length ratio, Lr = Lm/Lp
- Ar = Lr^2
- Vr = Lr^3
What are kinematics?
They are quantities that depend on time bu not on mass
What are some fundamental dimensions of kinematic quantities?
What is some kinematic ratios?
Ratios are dimensionless and allow models and prototypes to be scaled appropriately by these ratios.
- Velocity ratio, Vr = Vm/Vp = const
- Qr (volumetric flow rate ratio) = Qm/Qp = ArVr(velocity ratio)
- Tr = Tm/Tp = LrVr^-1
What are some fundamental dimensions for dynamic quantities?
What is some dynamic ratios?
Ratios are dimensionless and allow models and prototypes to be scaled appropriately by these ratios.
- Fr = Fm/Fp = Mr ar = ρr Lr^2 Vr^2
- Wr = Wm/Wp = FrLr = ρr L^3 Vr^2
True or false:
We can ignore (+) or (-) symbols along with coefficients like 1/2 or 1/4 in our fundamental dimension representations.
True, ignore the symbols, the dimensions don’t half or have a positive or negative they are simly dimensions.
What is Reynolds number?
Reynolds number concerns viscous and inertia forces:
Re = ρvd/μ
It’s a ratio so dimensinoless used to scale flow conditions.
- ρ = density
- v = velocity of fluid
- d = characteritic length (i.e. pipe or chord length)
- μ = dynamic viscosity
True or false:
Coefficients are dimensionless
False. They are often dimensionless but not always.
How do we balance dimensions and get the correct units to forumals?
- For homogenity: must have smae units and dimensions on both sides. Must balance.
State some Key scaling ratios.
