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Flow through Chamfered Ducts

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shape factor
1
Consider the fluid flow through a chamfered duct. The flow velocity in the cross section satisfies the equation:
2
∂
v
z
∂
2
x
+
2
∂
v
z
∂
2
y
=
1
μ
∂P
∂z
=-10
.
The associated boundary conditions are
v
z
=0
(no slip condition) on the walls of the chamfered duct (colored black in the snapshots). These walls are defined by the implicit equation
α
6
x
+
4
y
=1
, where
α
is a parameter that determines the shape of the duct.
This Demonstration uses the finite element method in Mathematica's built-in function NDSolve to display the velocity distribution for values of
α
set by the user.
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