Velocity first, because it sets everything else
One GPM is 231 cubic inches a minute, and turning that into feet per second means dividing by 720 as well as by the bore area — 231 over 720 is 0.3208, and that is the whole conversion. Ten GPM through a half inch bore is 0.3208 × 10 ÷ 0.1963, which is 16.34 ft/s.
Get that factor wrong and every number downstream is wrong by a large integer, which is easy to do and hard to notice, because a velocity that is off by a factor of a few still looks like a velocity.
Hydraulic oil usually flows laminar, and that changes the rules
Reynolds number for a round bore in these units is 7,740 × velocity in ft/s × bore in inches ÷ viscosity in cSt. The default run — 16.34 ft/s through a half inch of 32 cSt oil — gives 1,976, which is below the 2,000 where laminar flow ends. The same numbers in water at 1 cSt would give 63,000 and be firmly turbulent.
Below 2,000 the friction factor is exactly 64 divided by the Reynolds number and the roughness of the bore drops out of the arithmetic entirely. Substitute that back into Darcy and the whole thing collapses to Hagen-Poiseuille: pressure drop proportional to viscosity, to length and to flow, and inversely proportional to the fourth power of the bore. The table on the page shows that fourth power directly — halve the bore at a fixed flow and the drop goes up sixteen times, every time both rows land laminar.
What the default run costs
Twenty-five feet of half inch hose with four sharp bends at 30 diameters each is 30 ft of equivalent bore. At 10 GPM and 32 cSt that is 36.5 psi, or 12.2 psi per ten feet, and 0.213 horsepower turned into heat — 542 BTU an hour out of one hose.
Move to three quarter inch and the table shows 7.8 psi. That is a bit over a fifth of the loss for a bore half again as large. It is not quite the clean fourth power — 1.5 to the fourth is 5.06, and 36.5 over 7.8 is 4.68 — and the gap is the bends: they are counted in bore diameters, so the 3/4 in run comes out 32.5 equivalent feet against 30 for the half inch. Hold the length fixed at 30 ft and the 3/4 in figure is 7.2 psi, which is the 5.06 exactly. Either way it is the argument for the larger hose on any line that runs continuously rather than in short bursts.
Viscosity does not push the drop one way
This is the part that surprises people who expect thin oil to be free. At this bore and flow, 220 cSt cold oil drops 250.9 psi and 32 cSt warm oil drops 36.5, which is the expected direction. But 15 cSt drops 44.2 — more than the 32 cSt figure, not less — because at 15 cSt the flow has gone turbulent, and a turbulent friction factor at that Reynolds number is higher than the laminar one would have been.
So the minimum sits near the transition band rather than at the thin end. The page computes where the low point falls for whatever you enter rather than stating a rule, because it moves with the bore and the flow. None of this says anything about which oil belongs in a machine — that is set by the pump inlet, the component data sheets and the temperature range the machine works over.
Cold starts are a different machine
Run 220 cSt through the default line and the pressure drop is nearly seven times the warm figure, and it is drawn straight off the pump output before anything moves. That is why functions are slow and heavy for the first few minutes and why a relief valve can be lifting on a cold morning at loads that do nothing when the oil is warm. The heat that produces is also what ends the condition, which is the only self-correcting thing about it.
Where this model stops
It treats hose as smooth round bore of a constant diameter. A hose bore grows a little under pressure and a reinforcement layer is not glass. Equivalent length per bend is a handbook approximation that depends on the fitting geometry, which is why it is a field on the form. Quick couplers, cartridge valves and filters are better handled with a psi figure from their own data sheet at your flow, and there is a field for that too. And nothing on the page speaks to what a hose is rated for — that is on the layline and in the maker data sheet.
Questions people ask
How do I convert GPM to velocity in feet per second?
Multiply the flow in GPM by 0.3208 and divide by the bore area in square inches. The 0.3208 is 231 cubic inches per gallon divided by 720, which converts minutes to seconds and inches to feet in one step. Ten GPM through a half inch bore of 0.1963 sq in gives 16.34 ft/s. Getting that factor wrong is the classic hydraulics unit error and the result still looks plausible, so it is worth checking against a known case.
Is hydraulic oil flow laminar or turbulent?
Usually laminar, which is the opposite of water in plumbing. Reynolds number is 7,740 times velocity in ft/s times bore in inches divided by viscosity in cSt, and 32 cSt oil at 16 ft/s in a half inch bore comes out near 1,976 — below the 2,000 where laminar ends. Water at the same velocity and bore would be over 60,000. The page prints the number rather than assuming a regime, because a hot machine and a cold one can sit on opposite sides of it.
Why does going up one hose size cut the pressure drop so much?
Because in laminar flow the drop goes as the fourth power of the bore at a fixed flow, and 1.5 to the fourth is 5.06. Half inch to three quarter inch over the same 30 ft of equivalent length takes 36.5 psi down to 7.2 psi. The table on the page shows 7.8 rather than 7.2, because it also lengthens the bends: they are counted in bore diameters, so a wider bore makes them physically longer. In turbulent flow the exponent is steeper still, nearer four and three quarters.
Does thinner oil always mean less pressure drop?
No, and the page shows why. Thinner oil lowers the laminar drop, but past a point it tips the flow into turbulence and the friction factor jumps. On the default run 32 cSt gives 36.5 psi and 15 cSt gives 44.2 psi, which is worse. The minimum sits near the transition band, and where that falls depends on the bore and the flow, so the page works it out rather than declaring a rule.
How much heat does a hose pressure drop make?
Pressure drop times flow divided by 1,714 is horsepower, and one horsepower is 2,544 BTU an hour. The default run at 36.5 psi and 10 GPM is 0.213 hp, or 542 BTU an hour, from a single hose. That is small on its own and it stops being small once every line, filter, coupler and valve in the circuit is added up, which is where an oil temperature problem usually comes from.
How do I count bends and fittings in a hose run?
As equivalent length: a number of bore diameters of straight hose that would cost the same. A sharp 90 degree elbow sits near 30 diameters in handbook tables and a swept bend far lower, but it depends on the specific fitting, which is why the figure is a field here rather than a constant. Where a maker publishes a component loss in psi at your flow, use that number instead, in the separate field.