Hi I need to calculate the length of a sonic nozzle, with exit radius = 12.7 mm(0.5 inch). This is the only information given. assuming gamma=1.4 There are relations for the contraction ratio Ax/At in terms of Mx anf gammma. Here Ax= area at any location before the throat At= area at throat Mx= Mach number at location x. I picked an arbitrary value for Mx = 0.2 and got a value for Ax, but how do I get the length of the converging section. Any help is appreciated Thank you.

Length is arbitrary - it doesn't affect the flow behavior. That's why only the area ratio is expressed in terms of Mach number. If you consider viscous flow there will be a small effect due to boundary layer growth, but I am assuming that you are looking only at inviscid flow.

If it is a sonic nozzle then the one dimensional isentropic analysis should suffice - ignoring viscous effect such as the boundary layer. If it is a de-Laval type nozzle then as along as the divergence angle of the nozzle isn't so great as to induce flow separation the 1D analysis should still hold.

Shuo