hi every body who can help me? any material about derivation of governing equations for flow nozzle; is any difference between axisymetric(general flow equations in cylindrical equations)equations and nozzle flow equations ? best regrads

For the derivation of the quasi-one-dimensional flow equations, I recommend John Anderson's books.

There is a difference between calculating a quasi-one-dimensional flow and an inviscid, axisymetric flow. The Q1D technique assumes that the area changes, but the flow itself is one-dimensional. That is a physically impossible scenario, and it leads to errors whenever the area gradient becomes large. In that situation, the axisymetric model will yield more accurate results.

Rich

The drivation, starting from the full Euler equations is essentially the same as that for the shallow water equations which is covered in most text books on perturbation methods. The advantage of the perturbation approach, as opposed to a more heuristic one, is that it makes precise the assumptions on the derivation and gives a means of determining the error in the approximation (and hence the possibility of improving the accuracy). The basic assumption of the nozzle equation is that the change in radius of the pipe is slow; i.e. if the radius of the pipe is r=R(z) then dR/dz should be small.

Are your nozzle is axisymmetric or 2D(two profiled walls and two parallel walls with rectangular cross section?

Since you mentioned axisymmetry and cylindrical coordinates, it doesn't seem like your're looking for the quasi 1-D equations, although you should really be more specific in your question.

Yes, you can use the "general cylindrical flow equations". The boundary conditions (not just equations) will determine what case you are running, i.e. you need an inlet condition, an outlet condition, and a wall condition. If your nozzle is not axisymmetric you can use cartesian coordinates.