Creeping Flow past a Sphere
John Steven Newman, Vincent Battaglia · 2020
The equations of motion of an incompressible fluid with constant viscosity are given by Eqs. 13.2 and 13.5 . A dimensionless statement of the problem of steady, uniform streaming past a body would be 18.1 Re 2 v * ⋅ ∇ * v * = − ∇ P * + ∇ * 2 v * , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108292/7aca7163-8572-4219-aada-d947e06364ff/content/math18_1_B.tif"/> 18.2 ∇ * ⋅ v * = 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108292/7aca7163-8572-4219-aada-d947e06364ff/content/math18_2_B.tif"/> with boundary conditions 18.3 v * = 0 o n t h e b o d y , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108292/7aca7163-8572-4219-aada-d947e06364ff/content/math18_3_B.tif"/> 18.4 P * = 0 v * = e x } a t inf i n i t y , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108292/7aca7163-8572-4219-aada-d947e06364ff/content/math18_4_B.tif"/> where 18.5 v * = v / υ ∞ , r * = r / R , P * = P − P ∞ μ υ ∞ / R , Re = 2 R ρ υ ∞ μ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108292/7aca7163-8572-4219-aada-d947e06364ff/content/math18_5_B.tif"/>