The speed of light in still water is c/u where u is the refractive index of the water. What is the speed of light in a stream of water flowing at a steady speed of v relative to the observer ? please explain briefly ?

This is Fizeau Experiment.
The speed of light gets changed when the medium is moving(except vacuum). This is properly explained in Special Theory of Relativity, Albert Einstein.
If you want to know further about then you must know the theory of relativity.
Sorry that I can’t explain you much further as Relativity is not in class 12thsyllabus.
Let me know if I can help you in any other way.