Mechanical engineering

Pump power and head, NPSH, affinity laws, compressor power, torque and transmissions, pumping unit strokes per minute, vessel wall stress, bolt tightening torque, bearing life.

14 calculators

Pumps

Pump power: hydraulic, shaft and input

Hydraulic power from the flow rate and head, shaft power from the pump efficiency, power drawn from the supply, and the smallest motor rating with a margin.

P_h = ρ · g · Q · H

Pump head from gauge readings

The actual total head of a running pump from the suction and discharge pressures, the gauge height difference and the pipe velocities — to compare with the rated curve.

H = (p_d − p_s) / (ρ · g) + Δz + (v_d² − v_s²) / (2 · g)

Net positive suction head available (NPSHa)

Net positive suction head available (NPSHa) for a pump taking liquid from a tank, separator or vessel, and its margin over the NPSH required (NPSHr) from the pump curve.

NPSHa = (p_a − p_v) / (ρ · g) + z − h_f

Pump affinity laws: speed and impeller trim

Flow rate, head and power of a centrifugal pump at another speed — including an ESP or a pump on a variable speed drive — and with a trimmed impeller.

Q_2 = Q_1 · (n_2 / n_1) · (D_2 / D_1)

Compressors

Compressor power and discharge temperature

Gas compression power in one stage or several stages with intercooling — from the isentropic or polytropic efficiency with the gas compressibility — the pressure ratio per stage and the discharge temperature.

ε = (p_2 / p_1)^(1/N)

Number of compressor stages

The fewest stages for a total pressure ratio, limited by the ratio per stage and by the discharge temperature; the pressure ratio and discharge temperature of each stage.

ε_T = (1 + η_s · (T_max / T_1 − 1))^(k/(k−1))

Drives and transmissions

Shaft torque and shaft diameter

Torque from the transmitted power and speed — for a motor, pump, gearbox or coupling — and the smallest diameter of a solid shaft for an allowable torsional stress.

T = P / ω = 9549 · P / n

Pumping unit strokes per minute and motor sheave

Strokes per minute from the motor speed, the V-belt sheave diameters and the gearbox ratio, and the motor sheave diameter for a required stroke rate.

N = n_m · (d_m / d_r) · (1 − ε) / i

Rolling bearing rating life L10 (ISO 281)

Basic rating life of a bearing in millions of revolutions and in operating hours from the dynamic load rating and the equivalent load, and the life at a higher reliability.

L_10 = (C / P)^p

Strength and bolting

Pressure vessel shell: wall stresses and thickness

Hoop and longitudinal stresses in the cylindrical shell of a vessel or pipe under internal pressure, the required wall thickness and the allowable pressure per GOST 34233.2 with the weld joint efficiency and allowances.

σ_t = p · (D + s − c) / (2 · (s − c))

Bolt tightening torque

Tightening torque for a required preload — as a share of the bolt's yield strength — through the nut factor K, which covers the friction in the thread and under the nut.

A_s = π/4 · (d − 0.9382 · P)² (UN: d − 0.9743 · P)

Bolt preload from tightening torque

Preload and stress in a bolt or stud for a known wrench torque, and their share of the yield strength.

F = T / (K · d)

Other areas

Sucker-rod pump displacement

Theoretical and actual displacement of a sucker-rod pump from the plunger diameter, stroke length and pumping speed, with the volumetric efficiency.

Q_t = 1440 · (π · D² / 4) · S · nFrom Oil and gas production

ESP: total dynamic head, stages and power

Required ESP head from the fluid level, the wellhead pressures and the tubing friction; the number of stages from the head per stage, the hydraulic power, the shaft power and the electrical input of the submersible motor.

H = H_dyn + (P_wh − P_c) / (ρ · g) + h_frFrom Oil and gas production

Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.