I am working on an electric ducted fan rocket that has thrust vector control, see image 1. The 90mm EDF is located a bit higher above this blue section, near 1., so I believe the blue section becomes a "thrust tube". Both the EDF tube housing and "thrust tube" are 90mm in diameter
For a given static thrust (3.62kg in my case),I am interested in the maths behind finding the velocity exiting the annular area, V1, the velocity at the exit of the "thrust tube", V2 and why the EDF thrust varies depending on the thrust tubes exit area. I had seen a formula that can find this V1 velocity . M_dot can be expanded to densityAreaV1, where Area= annular area of EDF or FSA.
On the velocity note, another confusion arose in me. If there was no thrust tube, I could find V1 using the first equation for the given static thrust. The area would be the annular/FSA area of the EDF. With the thrust tube, I would think the same formula and values would apply, getting V1. But if the thrust tube exit area affects the overall thrust, there must be some relation to and the the 1st formula.
Edit: In short, my goal was to find the velocity at the EDF exit. I was to use this value as an initial condition for a CFD analysis( to determine the values for redirected thrust), seen attached. . Equations for EDF thrust involved knowing the overall thrust, made of the propeller thrust and force developed by the duct interior. The problem is that the EDF thrust (3.62kg) is specified for solely the EDF; my scenario has an additional extension, so the actual overall thrust is unknown ,leading to being unable to find the EDF exit velocity
I would appreciate any advice