Question

The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the incompressible limit, the density of the fluid may be regarded as a constant, and the system of equations becomes, Because of the non-linearities, there are very few exact solutions that are known for these equations. One of the exact solutions is pressure-driven channel (or pipe) flow, also known as Poiseuille flow. In this flow, all solid, no-slip walls are parallel to the x-axis, and the channel/pipe is sufficiently long that the velocity field does not vary in the axial direct (i.e. it is "fully developed"). For these conditions in a two-dimensional channel, the Navier-Stokes equations can be reduced to a single-equation describing the axial velocity distribution along the height of the channel, where the pressure gradient is a constant parameter. Once the solution reaches steady state, the velocity distribution is parabolic, that is, h2 dP 8p dx where the channel's vertical extent is y = [0,h] and UO is the velocity at the channel centerline. The full solution to the unsteady problem can be found by decomposing the velocity into a steady state and a transient component as so that which may be treated with separation of variables.

Answer 1

S Give ttt Qu 16 Id dt 볶 to-foto 왔 ニー-p(3345)

92)+3