quiz2 - V . Equation of continuity, cylindrical coordinates...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Quiz #2 ECH 3203, Fall 2010 Friday, September 24 Directions: Thirty minutes. Closed book. No notes. No calculator neededed. Maximize your score by showing all work. Good luck to you!! Lubrication of a piston A solid, cylindrical piston with radius R p is centered in a tube of radius R t . Applying a force on the piston in the axial ( z ) direction causes the piston to move with constant velocity V . The gap between the piston and the tube is Flled with a Newtonian ±uid of known viscosity μ and constant density ρ . ²ind the force necessary to move the piston with constant velocity V . a) Clearly write the governing di³erential equation for this problem along with the boundary conditions. b) Calculate the velocity u z as a function of radial position for R p < r < R t . c) Calculate the shear stress τ rz as a function of r . d) Now use the shear stress calculation to Fnd the force (per unit length of piston) necessary to move the piston with the speciFed velocity
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: V . Equation of continuity, cylindrical coordinates t + 1 r r ( ru r ) + 1 r ( u ) + z ( u z ) = 0 Navier-Stokes equations, cylindrical coordinates r-momentum: p u r t + u r u r r + u r u r -u 2 r + u z u r z P = b r p 1 r r ( ru r ) P + 1 r 2 2 u r 2-2 r 2 u + 2 u r z 2 B-P r + g r -momentum: p u t + u r u r + u r u + u z u z + u r u r P = b r p 1 r r ( ru ) P + 1 r 2 2 u 2 + 2 r 2 u r + 2 u z 2 B-1 r P + g z-momentum: p u z t + u r u z r + u r u z + u z u z z P = b 1 r r p r u z r P + 1 r 2 2 u z 2 + 2 u z z 2 B-P z + g z...
View Full Document

Page1 / 2

quiz2 - V . Equation of continuity, cylindrical coordinates...

This preview shows document pages 1 - 2. Sign up to view the full document.

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