And where is the weight of the vehicle, the width of the tire in that calculation?
295/75R22.5 LR “H” when run as a dual is rated at 6,005 lbs. at 120 psi. That's about the max for truck tires.
None of that matters. What matters is the pressure per unit area. Water will resist being moved. Above a certain psi, the tire wins and pushes the water out of the way. Above a certain speed, the water will push the tire up and you'll hydroplane.
Remember how I prefaced my original:
"Tire Pressure and Hydroplaning. If all else is equal (tread depth, tread design, water depth, etc.) a higher pressure WILL prevent hydroplaning at a faster speed than a lower pressure tire."
Let's say your truck weighs 10,000 lbs. (You've got a load of gravel.) And, that load is evenly distributed. Each tire carries 2,500 lbs.
If your tires are at 36 psi, then their contact patch will be sized: 2,500 lbs / (36 lbs/in^2) = 69.4 square inches of contact. Each inch has 36 psi. So, if your tire is a 295 width ( 25.4mm to 1 inch) then the contact patch will be ~ 11.6" wide (the 295mm) by ~6" long. A wide, short contact patch. But, each and every inch that pushes on water is only at 36 psi.
Now, you dump the gravel. Your truck weighs 6,000 lbs, evenly loaded. Same maths. 1,500 lbs per wheel at 36 psi = 41.6 in^2 contact patch. Given your tire width, that means the patch is the same ~11.6" wide by ~3.5" long. A VERY short patch. But, each and every inch that pushes on water is only at 36 psi.
Both cases, the water has a resistance based on speed. (Jump off a high bridge, water resists like concrete: you die. Jump off the edge of a dock, and it feels great.) In both cases above, the tire "cuts" into the water with 36 psi. Hydroplaning will result ~ 62 mph and above.
Wide tires only help by gaining "flotation" in soft surfaces (loam, sand, dirt). That, again, is dependent on psi. (Airing down in sand, etc., greater surface area, lower pressure against the soft surface.) Also, traction is greater in soft surfaces with wider contact patches than narrow ones.
If you're running narrow tires, the contact patch changes shape, from your wide/short to a narrow/long. There are benefits and tradeoffs to going with one shape over another (part of which is dependent on suspension geometry). But those all effect handling, wear, efficiency, etc., not hydroplaning.
But, overally, none of that matters with hydroplaning. The tread depth, pumping efficiency (related), water depth are variables. The PSI determines at what speed those factors cannot overcome water's physical characteristics.