WU3 - Problems of Size & Scale

Scaling

deals with the structural and functional consequences of changes in size or scale among otherwise similar organisms.

3 parameters changed when the size of a structure increases

Dimensions, material, design.

Geometrically similar triangles

if 2 triangles have all the same anges, their sides are in equal proportions, and the inverse is true as well.

L₂ = k_L * L₁ or L₂ / L₁ = k_L

relates geometrically similar triangles

Similarity ratio (scale factor), denoted k_L

term for the constant ratio between corresponding sides of similar figures

isometric

geometrically similar bodies

(L₂)² = (k_L)² * (L₁)²

uses the formula to express how surface area changes in relation to a changing dimension.

Plotting two variables on log coordinates

results in a straight line

Essential rule of using dimensions

equations hve to be dimensionally consistent or homogenous to be meaningful.

Poiseuille equation

Simplifies to just mass of fluid per unit of time, or M/T

Mass (M)

equivalent to length cubed, or L³