What does the annular area and velocity tool calculate?
The calculator on this page works in two clear stages. First it calculates the geometry: the annular area and radial clearance between the hole and whatever sits in the middle of it, whether drill pipe, a hammer body, a stabiliser or casing. Then it divides an air flow by that area to give velocity.
Keeping these stages separate matters because most real mistakes happen in one or the other. Geometry errors come from mixing millimetres and inches or confusing bit diameter with pipe diameter. Flow errors come from using the compressor’s free air delivery (FAD) as if it were the actual volume of air moving up the annulus under pressure.
The tool supports these modes:
- Geometry only: annular area and radial clearance for a given hole and pipe.
- Velocity: annular velocity from an actual volumetric flow at the annulus condition.
- Free air to actual flow: converts FAD to actual flow at a stated pressure and temperature before calculating velocity.
- Multi-section string: velocity in each section where hole or pipe diameter changes.
- Target flow: the free-air flow needed to reach a velocity you specify.
- Sensitivity: the effect of hole enlargement, a different pipe size or a change in flow.
The core formulas
Annular area: A = π/4 × (D_hole² − D_outer²)
Radial clearance: c = (D_hole − D_outer) / 2
Annular velocity: v = Q_actual / A
D_hole is the hole diameter at the section being checked. D_outer is the outside diameter of the drill pipe, hammer or other central body. Both must be in the same unit before squaring. Q_actual is the volumetric flow at the pressure and temperature in that section of the annulus.
The tool refuses to calculate when D_outer is equal to or larger than D_hole, because the area would be zero or negative. It also warns when the clearance is very small, since a tight annulus is sensitive to small diameter errors and to cuttings bridging.
Units: where most calculations go wrong
Indian drilling practice mixes units freely. Bits are often described in inches (6½ inch, 8 inch), pipe in inches or millimetres, compressors in cfm and pressure in psig or bar. The tool converts everything to SI internally and shows both sets of units in the result.
| Quantity | Common site unit | Conversion used |
|---|---|---|
| Diameter | inch | 1 inch = 25.4 mm |
| Flow | cfm (free air) | 1 m³/min = 35.31 cfm |
| Velocity | ft/min | 1 m/s = 196.85 ft/min |
| Pressure | psig | 1 bar ≈ 14.5 psi; absolute = gauge + atmospheric |
| Temperature | °C | K = °C + 273.15 |
Pressure conversions to actual flow always use absolute pressure. Using gauge pressure in a ratio is one of the most common errors and can overstate actual flow at depth by a large margin.
Why free air delivery cannot be used directly
A compressor’s FAD is the flow measured at inlet conditions, close to atmospheric. Once that air is compressed it occupies a smaller volume. In the annulus the air pressure is above atmospheric, highest near the bottom of the hole, and falls towards the surface. So the actual volumetric flow, and therefore the velocity, is lowest at the bottom and rises towards the top.
To convert, the tool uses the ideal-gas relationship:
Q_actual = FAD × (p_ref / p_actual) × (T_actual / T_ref)
with both pressures absolute. The pressure in the annulus depends on depth, cuttings load, any water inflow and back-pressure from the discharge, so it is a user input with a clear label, not a value the tool invents. If you do not know it, run the calculation at two or three assumed pressures and look at the range.
Worked example: a 6½ inch borewell
Consider a hole drilled with a 165 mm (about 6½ inch) bit on 114 mm (4½ inch) drill pipe, with a compressor delivering 900 cfm FAD (about 25.5 m³/min).
- Annular area: π/4 × (0.165² − 0.114²) = π/4 × 0.01423 ≈ 0.01118 m².
- Radial clearance: (165 − 114) / 2 = 25.5 mm.
- Flow near the surface, where pressure is close to atmospheric: 25.5 m³/min ÷ 60 ≈ 0.425 m³/s.
- Velocity near the surface: 0.425 ÷ 0.01118 ≈ 38 m/s, or about 7,500 ft/min.
- Near the bottom, if the annulus is at about 3 bar absolute and temperature is similar, actual flow is roughly a third, so velocity falls to about 12.7 m/s, or about 2,500 ft/min.
The same compressor gives two very different answers depending on where in the hole you look. Using FAD alone would suggest a comfortable 38 m/s everywhere, while the cuttings at the bit actually see much less.
Hole diameter is not always bit diameter
A bit drills a nominal size, but the hole is rarely exactly that size. In soft or weathered formations, overburden and fractured zones the hole can wash out and enlarge. In hard rock it may stay close to the bit size. Casing reduces the effective diameter in the cased section.
Enlargement has a strong effect because area depends on the square of diameter. In the example above, if the hole has opened to 175 mm, the area rises to about 0.01385 m² and the surface velocity falls from about 38 m/s to about 30.7 m/s, a drop of nearly a fifth from only 10 mm of enlargement. The sensitivity mode shows this so that you can judge how much margin your compressor really has.
Multi-section strings and the lowest-velocity section
Many strings are not uniform. The hammer may be larger than the pipe, a stabiliser may sit behind the hammer, and the upper hole may be cased or reamed. Each section has its own area and therefore its own velocity. The tool lists every section and highlights the lowest velocity, because that is where cuttings slow down, accumulate and cause regrinding or a stuck string.
| Section | Hole diameter | Outer diameter | What usually changes |
|---|---|---|---|
| Hammer and bit | Bit or slightly larger | Hammer body | Small clearance, high velocity |
| Open hole above hammer | Bit or washed-out size | Drill pipe | Often the lowest velocity |
| Cased section | Casing internal diameter | Drill pipe | Velocity rises again |
Choosing a velocity target
The tool does not impose one universal minimum velocity. The velocity needed to lift cuttings depends on their size and density, whether they are dry or wet, whether foam or water injection is used, and on depth. Drilling practice commonly quotes targets for dry air drilling in the region of 15–25 m/s (about 3,000–5,000 ft/min), with higher values for wet or heavy cuttings, but your hammer manufacturer’s and driller’s experience should set the figure.
The target-flow mode reverses the calculation. Enter a velocity and the tool gives the actual flow required, then the free-air flow at your stated annulus pressure. For the 165/114 mm example, 20 m/s near the surface needs about 13.4 m³/min, roughly 475 cfm FAD, but the requirement rises sharply if you want the same velocity at the bottom under pressure.
Limits of the calculation
- Velocity is an average across the annulus; real flow is slower near the walls and can be uneven in an off-centre string.
- The tool does not model the full pressure profile up the hole; it uses the pressures you enter.
- It does not predict hammer performance. Hammer air consumption at pressure is covered on our DTH hammer air requirement page.
- It does not account for air losses into fractured formations, which reduce the flow reaching the annulus.
- Water inflow and foam change cuttings transport in ways a simple velocity check cannot represent.
How Reddy Compressors helps
Borewell and DTH drilling is a core part of our work. We supply all types, all brands and all models of borewell compressors: new machines, used and refurbished units, rentals, service and spare parts. Typical borewell duty runs from about 600–1,500 cfm at 200–400 psig (13.8–27.6 bar), with special units up to about 35 bar (507.6 psig).
- We help rig owners and contractors check annular velocity and hammer demand together before choosing a compressor size and pressure.
- We sell and rent borewell compressors of ELGi, Atlas Copco, Ingersoll Rand, KAESER, Chicago Pneumatic, Doosan and other makes as an independent multi-brand specialist, not an authorised dealer. We have tie-ups with all major and reputed brands.
- Our service teams cover the whole of Telangana and Andhra Pradesh, and we supply machines and spares across India.
- When a compressor no longer delivers its rated FAD, we diagnose and repair it, because lost flow means lost velocity at the bit.
What to send us
- Bit size, drill pipe outside diameter and hammer size.
- Planned depth range and the formations you expect.
- Present compressor make, model, rated cfm and pressure, with a nameplate photo.
- Whether you use water or foam injection.
- Any problem you see: slow penetration, regrinding, stuck pipe or poor cleaning.
Frequently asked questions
How do you calculate annular velocity in a borewell?
Calculate the annular area as π/4 multiplied by the hole diameter squared minus the drill pipe outside diameter squared, using the same units for both. Then divide the actual air flow in the annulus by that area. Convert compressor free air delivery to actual flow at the annulus pressure first, using absolute pressure, otherwise the velocity will be overstated.
What annular velocity is needed to clean a DTH hole?
There is no single figure for every hole. Dry air drilling is commonly planned for roughly 15–25 m/s, about 3,000–5,000 ft/min, with more needed for wet, heavy or large cuttings and in washed-out holes. The hammer manufacturer’s guidance and the driller’s experience in the local formation should set the final target, and the calculation should be checked at the lowest-velocity section.
Why does a bigger compressor not always clean the hole better?
A larger cfm rating helps only if the extra air actually reaches the annulus at a useful velocity. If the hole has enlarged, area rises with the square of diameter and velocity drops. Air lost into fractures, worn compressor performance or restrictions also reduce delivered flow. Pressure must also be enough to operate the hammer and overcome water head, so flow and pressure must be checked together.
Can I use compressor cfm directly in the annular velocity formula?
Only as a rough upper estimate near the surface. Compressor cfm is free air delivery measured at inlet conditions. In the annulus the air is under pressure, so its actual volume is smaller, especially near the bottom of the hole. Convert FAD to actual flow using the ratio of absolute pressures and temperatures before dividing by annular area.
How does hole enlargement affect annular velocity?
Strongly, because annular area depends on the square of the hole diameter. In a 165 mm hole on 114 mm pipe, enlargement to 175 mm raises the area by nearly a quarter and cuts velocity by nearly a fifth for the same flow. Soft formations, overburden and fractured zones often wash out, so check sensitivity rather than relying on bit size alone.
What compressor size do I need for a 6½ inch borewell?
It depends on depth, formation, water level and the hammer you use, not only on hole size. Many 6½ inch borewell rigs in South India work with compressors in the 600–1,500 cfm range at 200–400 psig. Send us your bit, pipe, hammer and depth details and we will check annular velocity and hammer demand before recommending a machine to buy or hire.
Related pages
Calculators and worked examples
These tools give indicative figures for screening, comparison and for preparing an enquiry. They run in your browser and send nothing. No prices or tariffs are assumed: enter your own to see costs. Efficiencies and other figures shown are example values: replace them with your own. Results are not a performance guarantee or a design certificate; final selection is confirmed by a service engineer against the machine data sheet and the site.
Annular area and return velocity
The worked example below shows the method with fixed numbers. Turn on JavaScript to change the inputs.
Worked example
Inputs
- Hole diameter (mm): 115
- Rod outside diameter (mm): 89
- Free air supplied (m³/min): 12
- Bottom-hole back pressure (bar g): 1
- Target return velocity (m/s): 15
Result
- Annular area: 41.7 cm²
- Return velocity: 24.16 m/s = 4,757 ft/min
- Free air needed for the target velocity: 7.45 m³/min = 263 cfm at 15 m/s
- Assessment: Within the commonly quoted range
Method. Annular area = π/4 × (D_hole² − D_rod²). Actual flow at the back pressure = free air × (P_atm / (P_back + P_atm)). Velocity = actual flow ÷ area. A return velocity often quoted for efficient cuttings lift is around 15–25 m/s; confirm for your material.
What to take from it. Low return velocity leaves cuttings in the hole; very high velocity wears the rods and hammer. Both are warnings, not verdicts.
Technical content reviewed by D. Srinivas Reddy, Managing Partner and service engineer, Reddy Compressors. Last updated 17 October 2026. How our engineering content is reviewed.