One turn, one volume
The flighting sweeps the ring between its outside diameter and the centre pipe, and one revolution advances the material by one pitch. A 9 in screw on a 2.5 in pipe has an annulus of 58.7 sq in; at 9 in of pitch that is 528 cubic inches, or 0.3058 cubic feet, per turn with the trough completely full.
Nothing after that is difficult. At 45 percent trough loading and 400 rpm the screw moves 0.1376 cubic feet per turn and 24,000 turns an hour, which is 3,302 cubic feet an hour. A US dry bushel is 2,150.42 cubic inches, so that is 2,654 bushels an hour, and at 45 lb per cubic foot it is 74.3 tons an hour.
The centre pipe matters on small screws
A 2.5 in pipe inside a 9 in screw removes 4.9 sq in from a 63.6 sq in circle, which is 8 percent. Put the same pipe inside a 4 in screw and it removes 39 percent. That is why the pipe diameter is on the form rather than assumed away, and why capacity does not scale as the square of the screw diameter the way people expect.
Loading is the input nobody can look up
Everything above is geometry and is exact. The trough loading is not geometry: it is the fraction of the annulus that has material in it, and it depends on the material, on how hard the intake is being fed, on the incline, on flight wear and on the clearance to the tube. The table on the page runs from 15 to 90 percent, which is a factor of six in the answer, and picking a number off a page is not a substitute for a timed test with a scale under the discharge.
The commonest reason a real auger misses its catalogue figure is not speed and not wear. It is that the intake is not being fed hard enough to fill the trough, and no amount of rpm reaches material that is not in the flight.
Where linearity ends
Rate is linear in rpm right up until the point where the material is being flung against the tube instead of carried along it. Past that the loading collapses while the power and the wear keep climbing. Where the turn happens depends on diameter and material and is a supplier question. The same applies to inclines: capacity falls as the screw tips up because material falls back over the flight, and how fast it falls depends on the material and on the clearance, so the incline factor here is an input rather than a formula.
Questions people ask
How do you calculate the capacity of a screw conveyor?
Work out the annulus between the flight diameter and the centre pipe, multiply by one pitch to get the volume swept per revolution, then multiply by rpm, by 60, and by the trough loading fraction. A 9 in screw on a 2.5 in pipe at 9 in pitch sweeps 0.3058 cubic feet a turn, and at 45 percent loading and 400 rpm that is 3,302 cubic feet an hour.
How many bushels an hour will a 9 inch auger move?
It depends entirely on speed and trough loading, which is why both are inputs here. At 400 rpm and 45 percent loading the geometry gives 2,654 bushels an hour. At 30 percent loading the same auger at the same speed gives 1,769. The catalogue figure for any auger assumes a loading it rarely sees on a real intake.
What is trough loading and what number should I use?
It is the share of the swept annulus that actually has material in it. This page will not give you a value, because it is a property of your material and your intake rather than of the machine: abrasive, sticky and poorly flowing materials run lower, free-flowing grain runs higher, and an intake that is not being fed hard runs lower still. Get it from your screw supplier for your material, or time a known weight through the machine.
Why does my auger move less when I tip it up?
Material falls back over the flight instead of being carried forward, and the steeper it is the more falls back. How much capacity that costs depends on the material and on how tight the tube is to the flight, so the incline factor on this page is an input you supply from your supplier or your own test rather than something derived. A horizontal screw is 100 percent by definition here.
Does this tell me what motor the screw needs?
No. Screw conveyor power depends on the material factor, the length, the number and type of hangers and the loading, and it is a separate calculation belonging to the screw supplier. This page works out volume and mass rate from geometry and speed and stops there. It states no rated capacity, no speed limit and no manufacturer figure.