 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 3

The leading streamwise momentum equation in <lubrication theory> is
$$
0=-p_x+\mu u_{yy},
$$
with $p=p(x)$. The <no-slip boundary condition> is
$$
u(x,0)=U,\qquad u(x,h(x))=0.
$$
Twice integrating in $y$ gives the local <Couette-Poiseuille flow in a thin gap>
$$
\boxed{
u(x,y)=U\left(1-\frac yh\right)
+\frac{p_x}{2\mu}y(y-h).}
$$
Its volume flux per unit span is
$$
\boxed{
Q(x)=\int_0^hu\,dy
=\frac{Uh}{2}-\frac{h^3p_x}{12\mu}.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 38C / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 38C / b / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 38C / b / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)