On representation of expansion in fluid flow


by zhangwfjh
Tags: fluid, fluid dynamic maths, fluid dynamics, fluid flow
zhangwfjh
zhangwfjh is offline
#1
Sep1-13, 10:56 PM
P: 4
In Helmholtz original thesis On integrals of the hydrodynamical equations, which express vortex-motion, he mentioned in the first section that the change undergone by an arbitrary infinitesimal volume of water under the time dt is composed of three different motions. One of them is an expansion or contraction of the particle parallel to three main axes of dilatation. However in modern language, this part is represented by the negative gradient of a scalar function. My question is why the gradient which I think contains one direction can represent three main directions of dilatation?
Phys.Org News Partner Physics news on Phys.org
Sensitive detection method may help impede illicit nuclear trafficking
CERN: World-record current in a superconductor
Beam on target: CEBAF accelerator achieves 12 GeV commissioning milestone
boneh3ad
boneh3ad is offline
#2
Sep2-13, 12:03 AM
boneh3ad's Avatar
P: 1,437
Dilatation is usually expressed with a divergence, not a gradient, and the divergence has no direction.


Register to reply

Related Discussions
Fluid Flow Problem-Viscous Flow Mechanical Engineering 5
Fluid mechanics: Flow and velocity of a fluid Classical Physics 7
Fluid Mechanics: Inviscid flow v.s. Laminar flow Engineering, Comp Sci, & Technology Homework 1
Fluid flow Introductory Physics Homework 2
fluid flow Introductory Physics Homework 8