# Velocity Profile of a Flow

1. May 5, 2006

### Sophist

Stokes’ fluid is resting in a long channel, whose boundary planes are $$y = a$$ and $$y = -a$$ (which do not move). At time $$t = 0$$ a pressure gradient suddenly begins to act which is constant and equals $$G = G e_x$$. If body forces do not exist, and velocity is $$v = v (y, t) e_x$$, find the equation which $$v(y, t)$$ satisfies for $$t > 0$$, as well as boundary and beginning conditions for $$v(y, t)$$. When t --> inftinity v(y, t) is expected not to dependant on time t (motion becomes stationary). If we suppose that $$v(y,t) = V(y) + v_1 (y, t)$$, where $$V(y)=lim_{t-->infinity}v(y,t)$$ form the eqauation and boundary conditions that $$v_1 (y, t)$$ satisfies.