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authorClaudius "keldu" Holeksa <mail@keldu.de>2025-11-11 19:51:33 +0100
committerClaudius "keldu" Holeksa <mail@keldu.de>2025-11-11 19:51:33 +0100
commita49f595c42d6c26e8b130dc6487caeceb80d8775 (patch)
tree4cce277011b18b26012dafbf76b700cc5efdbf14 /typst
parent0f4d9cfbb2d87431afc6a7566bd0ec8d240263c3 (diff)
downloadphd-fluid_mechanics_report-a49f595c42d6c26e8b130dc6487caeceb80d8775.tar.gz
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Diffstat (limited to 'typst')
-rw-r--r--typst/main.typ7
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 ?