I need to answer HVAC and mechanical engineering questions. Please help me double-check my work.

I will attempt some of these problems during the week, and I will most likely finish the remainder over the weekend. I think I might have the right equations, charts, and literature to figure out these questions; there are inconsistencies in how the equations that I found in the literature (that I found online) are labeled that are making me nervous. These questions shouldn’t pose a problem to any HVAC professional who has experience. I need these questions answered: I have found equations online for number 1, number 2, and number 3; I have a textbook with examples that are probably going to be helpful for number 4. If you are an HVAC professional and not a mechanical engineer, you may skip number 4 ( I will either do this myself or find more specialized help for that question, if needed). There is something that bothers me in the equations that I am finding in HVAC and mechanical engineering literature that is making me second-guess myself; such problems include inconsistent labeling in equations, unknown units, no explanation as to the type of pressure (absolute, static, dynamic, etc.), and other loose ends unexplained that make me unconfident about using those equations. It is important that I have correct answers to these. In this particular case, friction is neglected, standard conditions are assumed, and everything is idealized; if these assumptions change (this is unlikely), I will let you know. When you message me for the first time, I will send out web links; these are weblinks to webpages that have equations that I think maybe relevant (they may be the exact equations I need, but there are issues with these equations that are making me second-guess them). I also might attach photos of drawings and textbook examples (if needed). I am currently gathering, archiving, and bookmarking these; when I am done gathering these, I will hand them over to you to take a quick look at the material I have gathered. We will coordinate through messaging each other online. These questions shouldn't take long for an HVAC professional. If you happen to know the answer off the top of your head, show how you arrived at your answer. 1. A fan delivers 1000 CFM @ 2" WC using 1 HP Motor. What happens if the static pressure becomes 1" WC? 2. Lift a 1000 lb item with a cable on a 1 ft. diameter drum from ground to 100 ft. elevation in 20 seconds a. What Motor size is necessary? b. The Motor (running at 1750 RPM) actuates the drum via a gear reducer. What reducing ratio is necessary? 3. A motor (running at 1750 RPM), through V-belt transmission, actuates a fan @ 1200 RPM. Assuming the motor sheave is 4" in diameter and the distance motor - fan centerline is 24" a. What diameter should the fan sheave have? b. What is the V-belt length? 4. A 4' long beam is supported (pinned) at the left end and at the mid point. Consider a 10,000 lb load vertical down: i. At mid distance between supports i.i. On the right end of beam i.i.i. On the left end of beam a. Calculate support reactions b. Sketch the bending moment diagram and calculate its values at supports, right end and mid distance between supports.