Fluids - Using Navier Stokes

[MidnightR]

Incompressible fluid of kinematic viscosity v and density p flows in the x direction between two parallel planes at y = +-h, under the action of an unsteady unidirectional pressure gradient -p(G +Qcosnt), where G, Q, n are constants. Verify that unidirectional motion is possible and that the x-component of velocity is...

I've been staring at my fluid notes for hours and it's got me no where. Someone, please, help, me, start. What are the boundary conditions?

Thank you!

*goes back to staring at fluids notes xD* Perhaps it will click eventually, there are a lot of examples but the lecturer just comes up with b.c. and I can't see where the heck they came from.

 

[lippyka]

The boundary conditions for this problem are that the velocity components at both planes (y = +-h) should be zero. This means that the flow is unidirectional, and that the x-component of velocity is constant across the two planes. The pressure gradient is given by -p(G + Qcosnt), where G, Q, and n are constants, so the pressure at the two planes should be equal. Therefore, the unidirectional motion is possible and the x-component of velocity is determined by the pressure gradient.