CE 319 F Daene Mc Kinney Elementary Mechanics

CE 319 F Daene Mc. Kinney Elementary Mechanics of Fluids Viscosity

Some Simple Flows • Flow between a fixed and a moving plate Fluid in contact with the plate has the same velocity as the plate u = x-direction component of velocity y Moving plate u=V V B Fluid Fixed plate x u=0

Some Simple Flows • Flow through a long, straight pipe Fluid in contact with the pipe wall has the same velocity as the wall u = x-direction component of velocity R r x V Fluid

Fluid Deformation • Flow between a fixed and a moving plate • Force causes plate to move with velocity V and the fluid deforms continuously. y Moving plate t 0 u=V t 1 t 2 Fluid Fixed plate x u=0

Fluid Deformation Shear stress on the plate is proportional to deformation rate of the fluid y d. L t da dy Moving plate u=V+d. V t+dt dx Fluid Fixed plate x u=V

Shear in Different Fluids • Shear-stress relations for different types of fluids • Newtonian fluids: linear relationship • Slope of line (coefficient of proportionality) is “viscosity”

Viscosity • Newton’s Law of Viscosity • Units • Water (@ 20 o. C) – • m = 1 x 10 -3 N-s/m 2 Air (@ 20 o. C) – • V+dv m = 1. 8 x 10 -5 N-s/m 2 Kinematic viscosity V

Flow between 2 plates Force is same on top and bottom Thus, slope of velocity profile is constant and velocity profile is a st. line y Moving plate u=V V B Fluid Fixed plate Force acting ON the plate x u=0

Flow between 2 plates Shear stress anywhere between plates y Moving plate V u=V t B t Fixed plate Shear on fluid x u=0

Flow between 2 plates • 2 different coordinate systems B r x y V x

Example: Journal Bearing • Given – – – Rotation rate, w = 1500 rpm d = 6 cm l = 40 cm D = 6. 02 cm SGoil = 0. 88 noil = 0. 003 m 2/s • Find: Torque and Power required to turn the bearing at the indicated speed.

Example: cont. • Assume: Linear velocity profile in oil film

Example: Rotating Disk • Assume linear velocity profile: d. V/dy=V/y=wr/y • Find shear stress