CHEN 3005 Lecture Notes - Lecture 9: Dynamic Pressure, Newtonian Fluid, Viscosity
8 Sep 2014
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Review: dp/dz = - g p - p0 = - g(z - z0) A n df = differential amount of force. Double underline = stress tensor differential amount of force stress tensor differential amount of surface area da = dxdyiz. 3 things that a stress tensor does (to the vector da: changes the size of da, rotate da. 1 and 2 are general properties of vectors: has to change units (this isn"t mathematical propertythis is physics) Pressure r = position in the fluid (because pressure could be different at different locations in the fluid) idenfactor if i = j otherwise. Viscous stress: for simple (newtonian) fluids transpose ata means viscosity. Above eqn = newton"s law of viscosity (works for things like water) But doesn"t work for things like polymers which get entangled and have elasticity; or quick sand. Chen transport page 4 gradient and velocity are both individually vectorstogether, they are tensors.
