Engineering lesson
Why annular velocity changes when the hole gets wider
At a fixed volumetric flow rate, average annular velocity decreases as the flow area increases. Use the difference between hole and pipe cross-sectional areas, not the hole area alone.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Continuity supplies the first explanation
For incompressible steady flow, Q = vA. An 8.5 in hole around 5 in pipe has a smaller open area than a 12.25 in hole around the same pipe, so the same 600 gpm travels faster through the smaller annulus.
This average velocity is not the local velocity everywhere. Pipe position, rheology and the walls create a velocity distribution across the gap.
Keep flow rate and velocity units distinct
Gallons per minute describe volume crossing a section per time. Feet per second describe speed. The site's field formula converts the supplied gpm and squared-inch diameters into ft/s. Multiply by 60 if reporting ft/min.
A fluid velocity comparison is a continuity calculation, not a prediction that cuttings will be transported. Inclination, slip, beds, particle size and rheology matter to cleaning.
Use local geometry
When hole size changes, calculate local area and velocity for each interval. One surface rate can therefore correspond to several velocities along the same flow path.
Compressibility or influx can also change local volumetric rate. The comparison here holds actual Q fixed to isolate the area effect.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Hole diameter (in) = 8.5. Average velocity (ft/s): 5.18726009; Average velocity (ft/min): 311.235605.
- Average velocity (ft/s)
Worked example
Continuity through changing hole sizes
Actual rate 600 US gpm, pipe OD 5 in, hole diameter varies. All local volume assumptions remain fixed.
Relation and unit basis
v = Q/[2.448(Dh² − Dp²)] ft/s; ft/min = 60v
This average speed is not a local velocity field or a cuttings-transport criterion.
1. Define the baseline
Hole diameter (in) = 8.5
Actual rate 600 US gpm, pipe OD 5 in, hole diameter varies. All local volume assumptions remain fixed.
2. Select the relation
v = Q/[2.448(Dh² − Dp²)] ft/s; ft/min = 60v
This average speed is not a local velocity field or a cuttings-transport criterion.
3. Substitute the values
600/[2.448 × (8.5² − 5²)] = 5.18726009 ft/s; multiply by 60 for ft/min
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Average velocity (ft/s) = 5.18726009; Average velocity (ft/min) = 311.235605
The wider local flow area lowers average speed at fixed actual Q.
Result and interpretation
Average velocity (ft/s) = 5.18726009; Average velocity (ft/min) = 311.235605
The wider local flow area lowers average speed at fixed actual Q.
Change only hole diameter and read the velocity in both ft/s and ft/min.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Hole diameter (in) | Average velocity (ft/s) | Average velocity (ft/min) |
|---|---|---|
| 6.5 | 14.20858 | 852.5149 |
| 7.5 | 7.843137 | 470.5882 |
| 8.5 | 5.18726 | 311.2356 |
| 10 | 3.267974 | 196.0784 |
| 12.25 | 1.959804 | 117.5883 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. If annular area doubles at fixed Q, what happens to average speed?
Show the worked answer
It halves because v = Q/A. This says nothing by itself about the local cuttings transport threshold.
2. Reproduce the baseline Average velocity (ft/s) without rounding intermediate values.
Show the worked answer
600/[2.448 × (8.5² − 5²)] = 5.18726009 ft/s; multiply by 60 for ft/min. Average velocity (ft/s) = 5.18726009. The wider local flow area lowers average speed at fixed actual Q.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Hole diameter (in) changes from 6.5 to 12.25. Other controls remain as stated in the premise. Average velocity (ft/s) changes from 14.208582 to 1.95980441.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. This average speed is not a local velocity field or a cuttings-transport criterion. The wider local flow area lowers average speed at fixed actual Q.
Before using the result
- Use hole ID and pipe OD.
- Label ft/s versus ft/min.
- Keep actual local volumetric rate consistent.
The wider local flow area lowers average speed at fixed actual Q.
Continue learning
Start with the broader workflow guide · Related method guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.