Chapter_Four_Part_One_web

Chapter_Four_Part_One_web - ENU 4133 Chapter 4, Part 1...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: ENU 4133 Chapter 4, Part 1 February 1, 2010 Chapter 4 Differential Relations for Fluid Flow In scope of Exam #1 and/or HW #4 and #5 I 4.1 acceleration field of a fluid I 4.2 differential mass conservation (continuity) I 4.3 differential momentum conservation I 4.3, 4.6, 4.10 Navier-Stokes equation and solutions I 4.5 differential energy equation Additional Chapter 4 material will be covered for Exam #2. Acceleration Field of a Fluid General velocity field (Cartesian coordinates Eulerian/fixed frame): ~ V ( ~ r , t ) = ~ iu ( ~ r , t ) + ~ jv ( ~ r , t ) + ~ kw ( ~ r , t ) (1) Acceleration field differentiate w/r/t t . ~ a = d ~ V dt = ~ i du dt + ~ j dv dt + ~ k dw dt (2) Note: total time derivatives, not partial derivative. Considering u / x component: du dt = u t + u x dx dt + u y dy dt + u z dz dt (3) du dt = u t + u u x + v u y + w u z (4) du dt = u t + ~ V u (5) Acceleration Field of a Fluid (2) du dt = u t + ~ V u (6) dv dt = v t + ~ V v (7) dw dt = w t + ~ V w (8) ~ a = d ~ V dt = ~ V t + ~ V ~ V (9) Acceleration composed of local and convective parts. In general, this is termed the substantial or material derivative, e.g. , of B (can be ~ B or ~ ~ B ): DB Dt = B t + ~ V B (10) Differential Mass Conservation Equation I Take control volume as differential volume dx dy dz = dV I Identify generation and destruction terms (hint: very easy) I Identify inflow and outflow terms I Compile terms & do a little math...
View Full Document

Page1 / 22

Chapter_Four_Part_One_web - ENU 4133 Chapter 4, Part 1...

This preview shows document pages 1 - 6. Sign up to view the full document.

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