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Diffstat (limited to 'typst/main.typ')
| -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 ? |