Pilot reported a ruptured hydraulic line the cockpit resulted in a gear up landing. The POH was inaccessible and contributed to the emergency extension procedures not be complied with.

Narrative

After pre-flight; departed ZZZ1 at approx. XA00. Climbed to approximately 2;000 feet MSL; 1;500 feet AGL and encountered a ruptured hydraulic line (approximately 5 minutes into flight) spewing pressurized hot fluid onto pilot's right foot causing burns through footwear. After assessing engine performance; pilot attempted to lower landing gear. The gear failed to operate. Performed fly-by at ZZZ to have a lineman perform a visual inspection of the gear. He stated it was not down. Pilot squawked 7700 and [requested priority handling] on 121.5. ATC handed pilot to ZZZ approach for better comms. Climbed to approximately 4;500 feet MSL and diverted to ZZZ (longer and wider runway than ZZZ1 and fire service on field). Pilot attempted to use checklists to perform emergency landing gear lowering. The full POH was in the airplane; but was inaccessible to the pilot. Condensed spiral bound checklist being used did not contain the procedures. Pilot attempted to the use the emergency hand pump to lower the gear; but operated the hand pump improperly. Pilot was unable to get the gear to lower. Pilot made safe 'belly' landing at ZZZ. No injury to pilot. The aircraft did not sustain substantial damage. Prop strike and belly skin damage only. The catastrophic system failure could have potentially been overcome by with the hand pump; but there is no assurance that all three gear would have been successfully locked. Upon ruptured hydraulic line; discovered by right foot burning; pilot feared it may have been engine oil and that he was about to lose the engine. It took about 10 seconds to determine the engine appeared to be running properly and that the gear would not cycle. Pilot feared something worse may have occurred in the engine compartment causing the line to rupture (fire; etc.). Pilot determined the best course of action was to make a landing as soon as possible. As previously stated; pilot did not have access to the full POH as it was in the rear baggage compartment; out of safe reach. With limited time in type; pilot was unable to recall the proper emergency gear procedure. While this was an unfortunate incident; the pilot has many take aways from the event: 1) Ensure the full POH is accessible to the pilot. 2) Ensure understanding of landing gear system and procedures prior to flight .3) Consider use of cell phone or airplane radio to request the assistance of related to emergency operations.4) Consider recency of dual instruction received when flying unfamiliar aircraft.