Condottiere said:
Volume isn't at such a premium that it's the primary factor in the equation.
You still need bunkerage to fuel the transition, so the driving factor has to be cost, and in the specific case of a (star)warship would be the cost of the rest of the components in relation to that of the jump drive and the capability it brings, plus the likelihood of damage.
It's one reason I'm sceptical about the utility of adding stealth to a cheap spacecraft, or an expensive one, unless it's meant to be an infiltration vehicle for a really important mission.
The thing that drives how fast you can pump fuel is literally the size of the pipes. That is your physical limitation on how fast you can pump liquid hydrogen (well that and your pump, but let's assume you put the right size pump with the right size fuel line). Fuel lines are waste space for a ship, but are still necessary. The space shuttle would receive fuel (liquid hydrogen or oxygen) from it's storage tanks at 1,300 gallon/minute.
1 Dton of space can hold about 14,000 liters, or 3,700 gallons (all numbers rounded). So 10 Dtons of Lhyd is equivalent to about 140,000 liters, or 37,000 gallons. At the listed amount above your fuel would need to pump at (1hour = 60 minute) at a measly 615 gallons/minute or 2,333 liters/minute. Your throughput could be pressurized more, though Lhyd is already under pressure, and the question would be could your pipes take the additional pressure or would they spring a leak? That's something to consider if you are in a hurry to refuel.
UNREP would be based on two separate numbers - liquid and solid transfer. You aren't running a hose down a corridor through airlocks for fuel - fuel is transferred via a hose. Solid transfer of items is going to be based on taking containers of hard goods between ships. And that's going to be transferred via pallets. It's basically two pallets per dton, or 40 pallets. Larger ships will have cargo airlocks designed to accept larger 2-3dton sized containers. Smaller ships will transfer via a pallet, or worst, crates moved individually. The USN has gotten this down to literally a science. Everything is pre-positioned on the supply vessel and then quickly transferred to the receiving vessel. The idea is to time the transfer of bulk goods with the fuel. Depending on the supply ship they may, or may not get munitions. Though underway munitions replenishment is not something that is done that much these days since we aren't at war, and cruise missiles and such are both expensive and they are usually in VLS launchers, which these days are only replenished back in port.
Just last month a Tico-class CG collided with it's supply ship. Operations in space should be much safer since no waves, though it's still possible to have an oopsie.
https://navaltoday.com/2019/02/06/us-navy-cruiser-dry-cargo-ship-collide-during-replenishment-at-sea-maneuver/