6.5 Similitude

MODEL

Model is similar with real object required in certain scale ratio. It is needed to be tested in laboratory with similar condition which is likely to be occurring in real phenomena. The size of the model might not be smaller than prototype.

PROTOTYPE

Prototype is an actual object that is in its full scale and needed to be reacting properly in real phenomena for mankind example like: ship, spillway structure in open channel.

However, scaling effect might affect the characteristic of a real-world prototype. Factor which lead to scale effect might be air concentration, Earth characteristics.

Advantages for using similarities.

1. Performances of object can be predicted.
2. Economics and easy to build, until it’s tested to reach a value.
3. Non-functional structure can be measured. Such as dam.

Perfect model-prototype similarity: Mechanical similarity

A physical scale model satisfying mechanical similarity is completely similar to its real-world prototype and involves no scale effects.

Mechanical similarity requires three criteria:

1. Geometric similarity
2. Kinematic similarity
3. Dynamic similarity

Geometric similarity

Boundaries between 2 flows are exact dilation (expand) or shrinkages of each other.

Length, Lp/Lm  = Lr

Area,   Ap/Am  = Ar

Volume, Vp/Vm  = Vr

Kinematic similarity

Streamlines between flows are exact dilation or shrinkage of each other.

Velocity scale ratio, Vr = Vp/Vm 

Discharge scale ratio, 

Acceleration scale ratio, 

Dynamic similarity

Corresponding forces at corresponding locations mutually parallel and have the same ratio of magnitudes. This ratio is the same for all sets of corresponding forces.

∑F = Fg + Fp + Fv + Fe + Ft  = Resultant

Therefore: Fg + Fp + Fv + Fe + Ft + Fi = 0

Where Fi = -resultant force

Where:

Gravitational force

 Fg = mg = ρgL^3

Pressure

 Fp = ΔpA = ΔpL^2

Viscosity

 Fv = μ(V/L)A = μ(V/L)L^2 = μVL

Elasticity

Fe  = EvA = EvL^2

Surface Tension

Ft  = σL

Inertia force

 Fi = ma = ρL^2v^2

In a general flow field, complete similarity between a model and prototype is achieved only when there is geometric, kinematic and formed dynamic similarity to perform for real life situation.

For further description about dimensionless quantities:

http://www.ipplm.pl/bib/nrl/fluid.pdf