A pressure gauge is a heat meter
Hydraulic power is flow times pressure. When pressure disappears without anything moving, that power has not gone anywhere except into the oil as temperature. So the drop between the pump outlet and the tank return, measured with the machine running and the functions still, converts directly: psi times GPM divided by 1,714 is horsepower, and a horsepower is 2,544 BTU an hour.
Five hundred psi at 20 GPM is 5.83 hp, which is 14,842 BTU an hour. That is 4.35 kW of heating, from a machine that is standing still. The one condition on the measurement is that nothing is being moved — pressure that lifts a load is spent rather than lost, and subtracting gauges while the machine works counts real work as waste.
How fast the oil climbs
Forty gallons at 80 percent full is 32 gallons of oil. At 0.87 specific gravity that is 232 pounds, and at 0.45 BTU per pound per degree it takes 104.6 BTU to raise the whole reservoir by one degree.
Divide 14,842 by 104.6 and the oil climbs 141.9 F an hour with nothing taking heat away — more than two degrees a minute. It never actually does that for a full hour, because the tank starts shedding heat to the air as soon as it is warmer than the air, but the first ten minutes are close to it. That number is the reason a small reservoir on a hard-working machine is a temperature problem rather than a capacity one.
What holding a temperature costs
Steady state is simple arithmetic: the heat going in has to equal the heat going out, and heat goes out in proportion to how far the oil sits above the air. Holding 140 F oil in 75 F air is a 65 degree difference, so 14,842 BTU an hour needs 228 BTU an hour for every degree of that difference.
Enter what your system already rejects and the page runs it the other way: at 150 BTU/h per degree, the same heat load settles at 174 F, because 14,842 divided by 150 is 99 degrees above the 75 F air. Neither figure is a verdict. What oil, seals, hoses and components tolerate is on their data sheets, and a cooler is specified at a stated oil flow, air flow and temperature difference together rather than by a single number.
Dwell time and the oil that is not in the tank
Thirty-two gallons at 20 GPM is a 1.6 minute dwell — the average time a gallon spends in the reservoir between trips through the system. That average hides a lot. Oil returning near the suction can go round again in seconds while oil in a corner sits all day, which is what baffles exist to prevent.
The other half of the volume question is the oil that leaves. Two 3 in bore cylinders on a 24 in stroke hold 339 cubic inches between them when they are fully out, and 60 ft of 3/4 in line holds another 318. That is 657 cubic inches, or 2.85 gallons, and it comes out of the tank. A 40 gallon tank at 80 percent drops to 73 percent full with everything extended, and a smaller tank on the same machine drops a great deal further — which is where suction problems start.
Where the estimate is thin
The system charge here counts cylinders at full stroke and the lines, and nothing else. Filters, coolers, valve bodies, motor cases, the pump and every fitting hold oil that is not in the list, and a maker figure for those beats any estimate. Specific heat drifts upward as oil gets hotter, so the rise-rate figure is slightly pessimistic at high temperature. And the whole heat calculation rests on one pressure reading taken under one condition — take it a few times, on a few days, before trusting it.
Questions people ask
How do I calculate the heat load in a hydraulic system?
Measure the pressure drop between the pump outlet and the tank return with the machine running and nothing moving, then multiply by the flow and divide by 1,714 for horsepower. Multiply by 2,544 for BTU an hour. Five hundred psi at 20 GPM is 5.83 hp, or 14,842 BTU an hour. Pressure that is actually moving a load is not part of this — that power leaves as work.
How fast does hydraulic oil heat up?
It depends entirely on how much oil there is. Thirty-two gallons at 0.87 specific gravity is 232 lb, and at 0.45 BTU per lb per degree that is 104.6 BTU per degree. A 14,842 BTU an hour load raises it 141.9 F an hour with no cooling at all — over two degrees a minute. Real machines shed heat as they warm, so the climb flattens, but the first minutes are close to the full rate.
How much cooling does a hydraulic system need?
Divide the heat load by how far above the air you want the oil to sit. Holding 140 F in 75 F air is 65 degrees, so 14,842 BTU an hour needs 228 BTU an hour per degree. A cooler data sheet quotes duty at a stated oil flow, air flow and temperature difference together, and the three go with the number. What temperature is acceptable for your oil and components is on their own data sheets, not here.
What is reservoir dwell time and does it matter?
It is tank volume divided by pump flow — 32 gallons at 20 GPM is 1.6 minutes. It is the average time a gallon spends in the tank shedding heat and letting air and water separate out. It is only an average: oil returning close to the suction can go straight round again, which is why baffles and separated return and suction positions matter more than the number itself.
How much oil does a hydraulic system hold outside the tank?
More than most people count. Two 3 in bore cylinders on a 24 in stroke hold 339 cubic inches fully extended and 60 ft of 3/4 in line holds 318, which is 2.85 gallons together. Filters, coolers, valve bodies and pump and motor cases hold more on top of that. It all comes out of the reservoir when the machine extends, and the tank level has to work at the lower figure.
Why does my hydraulic oil run hot when nothing is moving?
Because that is the condition that makes the most heat. Flow crossing a relief valve or a closed centre valve does no work at all, so the entire pump output turns into temperature. The table on the page shows it directly: heat scales straight with the pressure being thrown away. A stuck relief, a partly closed valve or a blocked filter all show up as oil temperature before they show up as anything else.