Register to reply

Navier-Stokes (Low-Re Spherical)

by alvi123
Tags: lowre, navierstokes, spherical
Share this thread:
Mar2-10, 03:34 PM
P: 1
My first time posting..

I am looking for guidance in how to solve this question : "Show that the pressure is a HARMONIC FUNCTION ([tex]\nabla^2 P = 0[/tex] I did that), and that the following solution [tex]P = P_{\infty}[/tex] - [tex]\mu\nabla\cdot[/tex] (U/r) where [tex]P_{\infty}[/tex] is the pressure far away from the sphere, is harmonic and satisfies the appropriate boundary conditions. "

Background : This is trying to find the velocity, pressure, vorticity and streamfunction of SLOW FLOW around a sphere. Assumptions are incompressible, steady flow and no slip. Boundary conditions are that when r = a [tex]V_{\theta} = 0[/tex] [tex]V_{r} = 0[/tex] where a is the radius of the sphere and U is the flow speed in the Z direction.

I thought i did ALL the work when i found the pressure, velocity, stream function and vorticity already, but when i solved for the supervisor said i didnt answer the question. To cut a 6 page derviation short, i will just give the results : [tex]\Psi = A/r + Br + Cr^{2}[/tex] , [tex]P_{\infty} - P = (3Ua\mu cos\vartheta)/2[/tex]
Phys.Org News Partner Physics news on
Engineers develop new sensor to detect tiny individual nanoparticles
Tiny particles have big potential in debate over nuclear proliferation
Ray tracing and beyond

Register to reply

Related Discussions
Navier Stokes? Calculus & Beyond Homework 0
Why is there a prize of $1 million for showing that there are . . . ? Differential Equations 4
What are Navier-stokes equations and why are they difficult to solve? General Math 5
Navier-Stokes equations Differential Equations 13
Navier Stokes: Spherical form Calculus 1