Practice and answer pack
Drilling hydraulics practice problems and answer sheet
Practice continuity, pressure-budget accounting and rheology conventions with explicit unit checks. The exercises distinguish calculated average speed from a hole-cleaning or friction model.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Start with a geometry and units ledger
Write the hole diameter, pipe OD, actual rate and requested velocity unit. Compute the open area before converting the rate. A rate expressed in gpm must be converted consistently with the squared-inch geometry.
The baseline worked example uses 600 gpm in an 8.5 in by 5 in annulus. Reverse-check by multiplying average velocity by open area.
Keep pressure contributions separate
For ECD exercises, identify annular friction, static fluid head and any surface boundary term. Use TVD for the equivalent-density conversion, while measured path length belongs to frictional intervals.
For friction-factor exercises, state Darcy or Fanning before using a numerical value. For rheology exercises, retain the shear-rate interval and the exponent-dependent units of consistency.
Explain what remains unknown
A completed arithmetic sheet still does not specify local cuttings slip, bed formation or a turbulent non-Newtonian pressure closure. State which additional information each of those questions requires.
Print the problems or download the synthetic values. The answer key includes units and interpretation so an instructor can distinguish a numerical slip from an incorrect physical model.
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.
Work the continuity case first, then compare the separate pressure and rheology questions in the answer pack.
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.
Practice problems and answer key
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. Which length belongs in ECD conversion and which belongs in frictional section loss?
Show the worked answer
Use TVD for the equivalent-density denominator and the measured flow-path interval for section friction.
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.
5. Convert Darcy f = 0.024 to the matching Fanning factor.
Show the worked answer
fF = fD/4 = 0.006. Use the factor with its corresponding pressure-loss equation.
6. Convert a 500 psi annular loss at 10,000 ft TVD to a density increment.
Show the worked answer
500/(0.052 × 10,000) = 0.961538 ppg. It is an increment, not the base mud density.
Before using the result
- Show the annular area calculation.
- Keep ft/s and ft/min distinct.
- State each model's regime and factor convention.
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.