fluidsnotes - Basic Fluid Mechanics for AOE 3204 This...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Basic Fluid Mechanics for AOE 3204 This section based on I. H. Shames, Mechanics of Fluids. Hydrodynamics Viscosity Viscosity is the property of a fluid which gives rise to shear stress when the fluid moves. Assume the fluid to be composed of layers moving relative to one another (this is called laminar flow). If one layer moves faster than the next (i.e., we have a velocity gradient), viscosity acts like friction between layers and causes a shear stress, t r . For example, think of a deck of cards sitting on a table. You push the top few and the ones below follow. The difference here is that a friction force depends on the normal force while viscous forces depend on the velocity difference between the layers. Going to a continuous medium (i.e., shrink the layers to zero thickness) this velocity difference becomes the velocity gradient , V n , where n is in the direction normal to the velocity vector. Newton’s Viscosity Law Shear stress is proportional to the velocity gradient. t r n V Velocity Profile
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 V n tm = where m is the absolute (or dynamic) viscosity . Units of Viscosity 2 2 FF A L L t 1 Lt Ft L V n V n t m t m = ”= \” e.g., 22 lb s dyn es or poise f t cm && , but 2 ML F t = so we can say 2 F t M L tM L tL m == 2 2 2 lb s slug e.g., = ft sec ft dyne s g = poise cm s c N s kg = m s m m ±² ³´ Ll = Remarks: 1. Fluids that obey Newton’s viscosity law are called Newtonian fluids. 2. Often m is divided by density to get kinematic viscosity , m n r = , with units ( ) 2 2 2 3 M L L t ft m , M sec t L s = 3. The viscosity is a function of the temperature of the fluid. 4. In a viscous fluid, no relative motion can take place between a fluid and a solid boundary, i.e., V fluid = V boundary at the boundary, this is called the “no-slip boundary condition.”
Background image of page 2
3 5. In the analysis of fluid flow, viscosity is often neglected. The fluid is said to be inviscid, i.e., it is assumed to have zero viscosity. This greatly simplifies the analysis. Example: Flow between parallel plates with the top plate moving at constant velocity V p and the lower plate stationary. p V Vy d = ²³ Ll What is the shear stress on the top plate? ( ) yd p V y V d tm m = == = if -5 2 f t lb sec 5 , d=3 in, = 2 1 0 (water) sec ft p V m , ( ) 5 4 2 5 2 10 .25 lb 4 10 ft t - - What is the shear stress on the bottom plate? Must be the same because the velocity profile is linear and hence the velocity gradient is independent of y . Stress Scalars, Vectors and Tensors Scalar A Scalar has only a magnitude (it’s just a number), for example, temperature or pressure. Vector A vector ha a magnitude and a direction. It is usually given in terms of 3 scalar components paired with unit vectors, for example, velocity, force. d V p x y
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 In Cartesian coordinates, x, y, z , ˆ ˆˆ xyz V V i V j Vk =++ r Where ˆ ,, i jk are the unit vectors in the x , y , and z directions respectively.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/05/2008 for the course AOE 3204 taught by Professor Dr.mccue during the Spring '08 term at Virginia Tech.

Page1 / 36

fluidsnotes - Basic Fluid Mechanics for AOE 3204 This...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online