drilling · hydraulics
Pump Output
click formula to derive ↑
Inputs
in
in
spm
Description
Computes circulating flow rate from mud pump liner diameter, stroke length, and pump speed, assuming a triplex (three-cylinder, single-acting) mud pump — the standard rig pump configuration. Establishes the flow rate that feeds every other hydraulics calculation in this cluster (Reynolds Number, Pressure Loss, Lag Time/Bottoms Up, and Bit Hydraulics all take Q as a direct input).
Variables
| Symbol | Unit | Description |
|---|---|---|
| Q | gpm | Flow Rate |
| D | in | Pump liner (cylinder) diameter. 165.1 mm (6.5 in) is a common triplex mud pump liner size; typical range is roughly 3-9 in. |
| L | in | Pump stroke length, a fixed mechanical property of the pump. |
| SPM | spm | Pump speed in strokes per minute. |
Assumptions
- Triplex (three-cylinder, single-acting) pump configuration — duplex (two-cylinder, double-acting) pumps use a different displacement formula
- 100% volumetric efficiency — actual pump output is typically reduced 90-98% by valve leakage and fluid compressibility; apply a manufacturer efficiency factor to this calculator's output if a precise field figure is needed
- Liner diameter and stroke length are the pump's actual current configuration, not a nameplate maximum
Limitations
- Does not model duplex pumps — many older or smaller rigs still use duplex pumps, which displace fluid on both the forward and return stroke with a different net-of-rod-volume formula
- No volumetric efficiency correction is applied — real-world pump output is consistently somewhat below this idealized value
- Does not account for multiple pumps operating in parallel — multiply this calculator's single-pump output by the number of pumps online if more than one is circulating
Use Cases
- → Hydraulics program flow-rate baseline: Establish the circulating flow rate available at a given pump speed before running Reynolds Number, Pressure Loss, or Bit Hydraulics calculations.
- → Pump speed planning: Determine the SPM required to achieve a target flow rate for hole cleaning or ECD management.
- → Multiple-pump rig hydraulics: Compute per-pump output as the building block for total rig circulating capacity when multiple pumps run in parallel.
Related Calculations
Region Notes
Permian Basin
Long-lateral wells commonly run pumps near 500-800 gpm to maintain adequate annular velocity for hole cleaning across a 2-3 mile measured depth.
Global
Triplex pumps dominate modern rig fleets; duplex pumps remain in service on some older or smaller land rigs and require a different displacement formula.
References
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