Hi chuck222,
Departmental scholarships vary in their policies and application approach by department. Each one sets their own rules and standards. If you are having trouble figuring out how to apply, I would reach out to any contact email you can find within Engineering and they will redirect you to the right person!
I would encourage you to go ahead and apply to a departmental scholarship. It never hurts to put your name in the hat. It seems like the most successful students apply their senior year of high school, so that they are awarded a 4-year scholarship through the department. This can be tacked on to any other scholarships you have from the University, so it would only help.
Personally, I applied to the Marine Science scholarships by filling out a few generic short-answer essays my senior year of high school. They selected a specific award and I was awarded a 4-year $2,000 scholarship. I have a fall dinner every year with my donor. It has been a wonderful experience.