progress

1 files changed, 10 insertions, 4 deletions

diff --git a/typst/main.typ b/typst/main.typ
index 546dbad..47724fc 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -40,7 +40,8 @@ Explores the effect of it in porous media and examines the more recent particle
 == Stokes Flow
 
 // Write about Navier
-The incompressible Navier Stokes equations are a set of equations
+The incompressible Navier Stokes equations are a set of equations defined with the density $rho$, the dynamic viscosity $mu$ and the
+velocity field $u(x,t)$
 
 #math.equation(
 block: true,
@@ -50,6 +51,9 @@ $ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f,\
 
 While we are often interested in Navier-Stokes flows, a generalized analytical solution does not exist,
 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
@@ -66,7 +70,7 @@ a far-field criterion
 
 == Solid-Fluid interaction with Stokes flow
 
-With the previous assumptions a solid sphere of radius $r$ moving with velocity $v$ in an unbounded creeping 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(
@@ -74,8 +78,10 @@ block: true,
 $ F = 6 pi mu r v $
 )
 
-where according to Proudman and Pearson@proudman_and_pearson the predicted drag is two percent lower than possibly more correct value
-by Proudman and Pearson@proudman_and_pearson.
+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