Shell Rotella T5 Synthetic Blend 15W-40

There exists a lot less expensive alternatives than the Rotella that are equally as good. The viscosity should be determined by the manufacturer's recommendation for the higher viscosity rating, most trans and hydraulic units cannot use the 40 rated viscosity. For instance, some hydro trans and hydraulic systems use a lower viscosity oil than an engine would need (most ATF is rated 10 with additional additives of course), Some hydros and hydraulic units use 10w-30 which is safe for most engines whereas some use ISO AW32 (rated viscosity is 10, again different additives) which is not safe for most engines.
Bottom line is if your hydro/hydraulic system recommends 10w-30 (the 30 in this viscosity is your most important factor for summer use) do not use a higher rated viscosity oil, if you plan on using the unit in winter months (the 10w in this viscosity rating is your most important factor for winter use) do not exceed that rating. If your engine would normally use SAE30 then the 10w-30 would be acceptable for winter use as well as summer use.

Very evident from your question and replies that oil weight information is not understood at all. Just forget single weight measurements! Single weight is a non starter even though Case might have said that 50 years ago. We are in the multi weight era. So lets start by saying the lower number is the start point!!! this is the point and viscosity when the oil is COLD and at rest. In most respects this can be ignored with the exception that higher weights create "drag" on the engine when starting. When starting in winter it is best that the drag is reduced as much as possible so the battery is not overloaded and resulting in slow starts (i.e. drains the battery). The moment the engine starts and starts to heat up the oil the viscosity changes! guess what it gets THICKER not thinner. A 20 start point might and could end up at 30, 40 50 or more as the oil heats with use.. So a requirement to run at 30 weight might actually be running at 50 weight with 15-50 oil. For me, I run at 5-50 summer and winter in WNY in my hydraulics and engine. Still not fully convinced that running the in my transmission is ok but getting there too. In closing you are A ok in using multi weight oils.

Just search on this site for oil types, viscosity major info from actual refineries. The lower number is the weight when COLD (i.e. 0 c) note that in warmer weather the oil viscosity will higher on startup . The higher number is the weight when HOT (78 c). In my transmission I use 5-50 synthetic in my hydraulic system summer and winter and change about every 3-5 years (no swap for seasons). The initial price of the oil is higher than conventional oils but over time, actually costs less as less frequent draining. I also use synthetic oil for my engine and run 15/30 year round. In the axle I still use gear oil.
So why use 5-50 in the hydraulic? for two important reasons:
1) The oil when cold is very thin and allows the engine to work less on starting when turning the pump. It also allows the oil to circulate quicker reducing the wear and it heats up quicker too.
2) The higher number provides more torque and is better for snow throwing/plowing, etc. I originally tried sticking with the Case recommendations but I quickly learnt when changing my hydraulic oil for the first winter season (5-20) that my snow caster did not throw snow as I expected. Changing the oil to 5-50, note the low number is still the Case recommended oil weight) significantly improved the caster snow throwing capabilities.