Annular velocity calculator
How fast mud comes up the gap between the pipe and the hole, and when the cuttings reach the shakers — with what the pipe not being centred does to both. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
This is arithmetic, not well control. Every figure here comes from a published definition and can be checked, and none of it accounts for temperature, compressibility, cuttings loading, gas cut or anything else a real well does. Pressure and hydraulics decisions belong to a drilling engineer with the well's own data.
The gap, not the hole
Mud goes up the space between the pipe and the hole, so the area that matters is the hole's area minus the pipe's. Forget the subtraction and the numbers still look plausible: an 8½″ hole with 5″ pipe gives 169.6 ft/min instead of 259.4, a factor of 1.53.
Which matters because of what the velocity is for: knowing when the cuttings reach the surface. At 10,000 ft that error is the difference between 39 minutes and 59. The cuttings arrive when they arrive.
24.5 is a rounding too
The usual form is
ft/min = 24.5 × gpm ÷ (D² − d²)
and like 0.052, that constant is not the constant. It falls out of the definitions: 231 cubic inches per gallon, times 4/π to turn a circle's area into a diameter-squared term, divided by 12 inches per foot —
231 × 4 ÷ π ÷ 12 = 24.50986123615188…
So 24.5 is 0.040% low. That is forty times smaller than the hydrostatic rounding and it points the other way, which is to say: it does not matter, and it is still worth knowing that it is a rounded number rather than a defined one. This page shows both.
The pipe is not in the middle of the hole
This is the assumption that actually costs something, and every annular velocity calculation makes it. Drill pipe does not sit centred in the hole — it lies against the low side, especially in a deviated well, and the annulus is eccentric.
Fluid takes the easy route, so it runs faster up the wide side and slower up the narrow. The number this page gives is an average: the real velocity on the narrow side is lower, sometimes far lower, and that is exactly how cuttings beds form on the low side of a deviated hole while the arithmetic says everything is being carried out.
And drilling mud is not water. It is shear-thinning, so its velocity profile is not the flat one this arithmetic assumes.
Bottoms-up time
Divide the depth by the velocity and you get the time for a cutting at the bit to reach the surface. It is the number the velocity exists to produce, and it is the one that gets used to decide when to look at the shakers.
It assumes a uniform annulus all the way up, which no real hole has — casing is wider than open hole, collars are fatter than pipe, and each section has its own velocity. For a real well the calculation is done section by section and added up.
Volumes here are in US gallons and barrels; a barrel is exactly 42 US gallons.