Centrifugal force pushes fluid outward, but the outer wall pushes back.
Given the assumptions:
vx(r)=r24μ(dpdx)+C1ln(r)+C2v sub x open paren r close paren equals the fraction with numerator r squared and denominator 4 mu end-fraction open paren d p over d x end-fraction close paren plus cap C sub 1 l n r plus cap C sub 2 Apply boundary conditions: At , the velocity must be finite, so . No-slip: At , . This gives advanced fluid mechanics problems and solutions
Advanced fluid mechanics bridges the gap between pure mathematics and practical engineering. By mastering these analytical and semi-empirical solutions, we can safely design everything from microscopic medical drug-delivery systems to massive transcontinental pipelines. Centrifugal force pushes fluid outward, but the outer