progress

1 files changed, 16 insertions, 11 deletions

diff --git a/typst/main.typ b/typst/main.typ
index b53fd0c..fa68f02 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -19,7 +19,7 @@
       email: "clho@norceresearch.no"
     ),
   ),
-  index-terms: ("Fluid Mechanics", "Review", "Writing Assignement Fluid Dynamics"),
+  index-terms: ("Fluid Mechanics", "Review", "Writing Exercise for Fluid Dynamics", "Writing Assignment for Fluid Dynamics"),
   bibliography: bibliography("refs.bib"),
   figure-supplement: [Fig.],
 )
@@ -75,9 +75,11 @@ $ "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
+where $U$ is the characteristic velocity and $L$ a characteristic length.
+When this number tends toward zero, the flow becomes dominated by viscous effects.
+And since we are mostly interested in low velocity and high viscosity cases we are able to
+disregard the inertial terms
+Which is why we arrive at the Stokes equations
 
 // Stokes
 #math.equation(
@@ -86,9 +88,9 @@ $ μ∇²u + f = ∇p,\
 ∇ · u = 0 $
 )
 
-An additional restriction by the creeping flow equations is the selection of boundary criteria where it depends on
-an infinite space with a set solid boundary interface.
-For simplicity a no-slip boundary condition is selected for the solid boundary.
+The Stokes equations are linear, enabling the principle of superposition, which allows for the combination of multiple solutions to construct
+complex flow fields.
+The original study for simplicity also included the boundary conditions
 
 #math.equation(
 block: true,
@@ -97,6 +99,9 @@ v arrow 0 "as" |x| arrow infinity
 $
 )
 
+These conditions allowed for an principal analysis of the effects a particle had in a field.
+In the next section we will specialize this for a sphere.
+
 == 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,
@@ -119,10 +124,10 @@ $
 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.
 
-//#math.equation(
-//block: true,
-//$ F = F_S ( 1 + (3/8)"Re" + (9/40)("Re")^2 * (log "Re" + gamma + (5/3) log 2 - (323/360)) + (27/80)*"Re"^3 log "Re" ) $
-//)
+#math.equation(
+block: true,
+$ F = F_S ( 1 + (3/8)"Re" + (9/40)("Re")^2 * (log "Re" + gamma + (5/3) log 2 - (323/360)) + (27/80)*"Re"^3 log "Re" ) $
+)
 
 //Using spherical coordinates $(r,theta,phi.alt)$ and no external force we receive the velocity components