Chapter_Four_Part_Three_web

Chapter_Four_Part_Three_web - ENU 4133 – Chapter 4, Part...

Info iconThis preview shows pages 1–7. 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 3 February 10, 2010 Chapter 4 – Differential Relations for Fluid Flow (Advanced Topics) In scope of Exam #2 I 4.7 – stream function I 4.8 – voriticity and irrotationality I 4.9 – frictionless, irrotational flows Stream Function When only two terms of the continuity equation are non-zero, it is possible to develop an equation for a single variable (the “stream function”, ψ ). Ignore cases where one of the non-zero terms is ∂ρ/∂ t . Incompressible, Cartesian: ∂ u ∂ x + ∂ v ∂ y = 0 (1) u = ∂ψ ∂ y (2) v =- ∂ψ ∂ x (3) ∂ ∂ x ∂ψ ∂ y + ∂ ∂ y- ∂ψ ∂ x = 0 (4) Steam Function (2) ~ V = ~ i ∂ψ ∂ y- ~ j ∂ψ ∂ x (5) ∇ × ~ V =- ~ k ∇ 2 ψ (6) ∇ × ~ V =- ~ k ∂ 2 ψ ∂ x 2 + ∂ 2 ψ ∂ y 2 (7) Stream Function along Streamline Along streamline in 2-D flow: dx u = dy v (8) udy- vdx = 0 (9) ∂ψ ∂ x dx + ∂ψ ∂ y dy = 0 (10) d ψ = 0 (11) Therefore, ψ is constant along a streamline. Other Cases Compressible, Cartesian:...
View Full Document

This note was uploaded on 07/14/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.

Page1 / 13

Chapter_Four_Part_Three_web - ENU 4133 – Chapter 4, Part...

This preview shows document pages 1 - 7. Sign up to view the full document.

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