Problem T7.2
A 2D steady, incompressible and inviscid flow field is described by the velocity potential function:
$\phi = xy$
i)
Determine the velocity field ($u = ?$ and $v = ?$)
ii)
Show that the continuity is satisfied.
iii) Attempt to sketch the constant value potential lines for the flow.
Hint: For any constant value of $\phi_i = C_i$ (where $i = 0$ to $n$), sketch $y = \phi_i/x$ on X-Y plane.
Remember: At any point $(x, y)$, the velocity vector is normal to the potential line
passing through $(x, y)$.
Equations:
Angular velocity:
Problem: T7.1
Definition of the velocity potential function $\phi$,
Problem: T7.2
$\omega_z = \frac{1}{2} \left(\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}\right)$
$u = \frac{\partial \phi}{\partial x}$,
$v = \frac{\partial \phi}{\partial y}$
and
$w = \frac{\partial \phi}{\partial z}$
