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| author | Claudius "keldu" Holeksa <mail@keldu.de> | 2025-11-11 19:51:33 +0100 |
|---|---|---|
| committer | Claudius "keldu" Holeksa <mail@keldu.de> | 2025-11-11 19:51:33 +0100 |
| commit | a49f595c42d6c26e8b130dc6487caeceb80d8775 (patch) | |
| tree | 4cce277011b18b26012dafbf76b700cc5efdbf14 /typst | |
| parent | 0f4d9cfbb2d87431afc6a7566bd0ec8d240263c3 (diff) | |
| download | phd-fluid_mechanics_report-a49f595c42d6c26e8b130dc6487caeceb80d8775.tar.gz | |
progress
Diffstat (limited to 'typst')
| -rw-r--r-- | typst/main.typ | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/typst/main.typ b/typst/main.typ index 47724fc..379a825 100644 --- a/typst/main.typ +++ b/typst/main.typ @@ -54,6 +54,7 @@ most analytical approaches rely on a set of restrictions or assumptions. With the Reynolds number defined by $ "Re" = (rho U L ) / mu $ + Luckily we decided to work on a fluid which tends $"Re" arrow 0$ or at least $"Re" << 1$ where due to the viscous forces the inertial term is negligable and is assumed to be zero. Which is why we arrive at this term @@ -68,21 +69,19 @@ $ μ∇²u + f = ∇p,\ An additional restriction by the creeping flow equations is the selection of boundary criteria where it depends on a far-field criterion -== Solid-Fluid interaction with Stokes flow +== Solid-Fluid single sphere interaction with Stokes flow With the previous assumptions a solid sphere of radius $r$ moving with a relative velocity $v$ in an unbounded creeping flow, we receive the drag force provided by Stokes #math.equation( block: true, -$ F = 6 pi mu r v $ +$ F_S = 6 pi mu r v $ ) where according to Proudman and Pearson@proudman_pearson_1957 at a Reynolds number of 0.05 the predicted drag is two percent lower than the possibly more correct value by Proudman and Pearson@proudman_pearson_1957. - - // Insert analytical solution // Different boundary examples ? |
