Slide 1

FLUID PROPERTIESIndependent variablesSCALARSVECTORSTENSORS

, u, w, vREFERENCE FRAMESCALARSNeed a single number to represent them: P, T,

besttofind.comTemperatureMay vary in any dimension x, y, z, t

www.physicalgeography.net/fundamentals/7d.htmlVECTORSHave length and directionNeed three numbers to represent them:

http://www.xcrysden.org/doc/vectorField.htmlUnit vector = vector whose length equals 1

xyz

VECTORSIn terms of the unit vector:

CONCEPTS RELATED TO VECTORSNabla operator:

Denotes spatial variability

Dot Product:

CONCEPTS RELATED TO VECTORSCrossProduct:

INDICIAL or TENSOR NOTATION

Vectoror First Order Tensor

Vector Dot Product

Matrixor Second Order Tensor

INDICIAL or TENSOR NOTATION

Gradient of Scalar

Gradient of VectorSecond Order Tensor

Special operator Kronecker Delta

TENSORS

Need nine numbers to represent them:

For a fluid at rest:

Normal (perpendicular) forces caused by pressure MATERIAL (or SUBSTANTIAL or PARTICLE) DERIVATIVE

FluidsDeform more easily than solidsHave no preferred shapeDeformation, or motion, is produced by a shear stress

zxu = molecular dynamic viscosity [Pas = kg/(ms)]Continuum ApproximationEven though matter is made of discrete particles, we can assume that matter is distributed continuously.This is because distance between molecules