laminar flow in a channel/pipe

stud

Dear friends, i am trying to simulate 2D laminar flow in a channel (including entrance length)using FV Method on colocated grid. for this following boundary conditions i have used

Inlet BC: , u-component = given, v-component =0,

Outlet BC: Pressure = given,i.e.pressure'=0.0, d(u,v)/dx=0 ie. u(i,j)=u(i-1,j) and so for v

at Walls u,v=0, dp'/dy=0

in case of pressure correction for cell just next to left boundary p'doesn't come into picture at left boundary as in continuity equation we can directly substitute u left value. then how to find this p'at left boundary as we need p at left boundary for calculating u at cell just next to left boundary. (this unknown p at left boundary becomes face value of p for cell just next to left boundary). i just tried by taking p'(1,j)=p'(2,j)...i got parabolic profile but with maximum value 3 time higher than uavg. ie.u at left boundary. at the same time i got some noises in the result at the right boundary. i think the right way is apply following equation to get p(1,j) from P(2,j) -dp/dx=-del.(mu*del_u)+rho*du/dt+del.(rho*V*u) then how to apply this at the fictious cell of zero volume at the left boundary. any suggestions