Drilling hydraulics practice problems and answer sheet
PetroCalcHub · Original synthetic teaching exercise · 2026-10-24

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.

Actual rate 600 US gpm, pipe OD 5 in, hole diameter varies. All local volume assumptions remain fixed.

1. Which length belongs in ECD conversion and which belongs in frictional section loss?

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2. Reproduce the baseline Average velocity (ft/s) without rounding intermediate values.

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3. Compare the first and last recorded scenarios. Which input changes?

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4. What would be needed to apply this example to a different physical system?

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5. Convert Darcy f = 0.024 to the matching Fanning factor.

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6. Convert a 500 psi annular loss at 10,000 ft TVD to a density increment.

Working: ________________________________________________


ANSWER KEY

1. Use TVD for the equivalent-density denominator and the measured flow-path interval for section friction.
2. 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. 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. 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. fF = fD/4 = 0.006. Use the factor with its corresponding pressure-loss equation.
6. 500/(0.052 × 10,000) = 0.961538 ppg. It is an increment, not the base mud density.

Method: Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Sources:
University of Iowa: Darcy friction and concentric annular flow: https://stern.lab.uiowa.edu/sites/stern.lab.uiowa.edu/files/2024-11/Chapter6_part1-58160-2024_final.pdf
SLB: annular velocity: https://glossary.slb.com/en/terms/a/annular_velocity