Midterm - z-direction through the annulus. Calculate the...

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

View Full Document Right Arrow Icon
Midterm Progress Assessment ECH 3203, Fall 2010 Wednesday, October 20 Directions: Two hours. Open book. No notes. No calculator needed. Maximize your score by showing all work. Good luck to you!! Problem #1: A Flow Meter Calculation (30 points) An inviscid fuid oF constant density ρ fows steadily through the contraction shown in the ±gure. Derive an expression For the fow rate Q in terms oF ρ , D 1 , D 2 , and h . Problem #2: (30 points) The velocity potential φ = - k ( x 2 - y 2 ) , where k is a constant, may be used to represent fow against an in±nite plane boundary as shown. ²or fow in the vicinity oF a stagnation point, it is Frequently assumed that the pressure gradient alonog the surFace is oF the Form ∂P ∂x = Ax, where A is a constant. Use the given velocity potential to show this is true.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Problem #3: Zero fow oF a fuid in an annulus (40 points) A solid, cylindrical piston with radius R p is centered in a tube of radius R t . The gap between the piston and the tube is Flled with a Newtonian ±uid of known viscosity μ and constant density ρ . A pressure drop, of P H - P L over the length L of the piston, drives a ±ow in the negative
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: z-direction through the annulus. Calculate the force F Z applied to the piston necessary to generate no net ow (volumetric owrate of zero). 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: u r t + u r u r r + u r u r -u 2 r + u z u r z = r 1 r r ( ru r ) + 1 r 2 2 u r 2-2 r 2 u + 2 u r z 2 -P r + g r -momentum: u t + u r u r + u r u + u z u z + u r u r = r 1 r r ( ru ) + 1 r 2 2 u 2 + 2 r 2 u r + 2 u z 2 -1 r P + g z-momentum: u z t + u r u z r + u r u z + u z u z z = 1 r r r u z r + 1 r 2 2 u z 2 + 2 u z z 2 -P z + g z...
View Full Document

This note was uploaded on 08/21/2011 for the course ECH 2023 taught by Professor Butler during the Fall '10 term at University of Florida.

Page1 / 2

Midterm - z-direction through the annulus. Calculate the...

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