Hydraulics Interactive engineering tool

Throat Bushing Flush Velocity Calculator

Determine average fluid velocity through a centered throat-bushing annulus from flow rate, diametrical clearance, and shaft diameter, or enter any three variables to solve for the fourth.

  • US + metric
  • Formula shown
  • Shareable results

Throat Bushing Flush Velocity

ft/s
gpm
in
in
Flush velocity 8.04 ft/s (average through annulus)
Bushing inside diameter (Ds + Cd) 2.06 in
Annular flow area 0.199 in²
Radial clearance (Cd / 2) 0.0313 in
Formula & method

A = π/4 · [(Ds + Cd)² − Ds²]  ·  Vf = Q/A

Db = 2 + 0.0625 = 2.0625 in
A = π/4 · (2.0625² − 2²) = 0.199 in²
Vf = 5 gpm / A = 8.04 ft/s

Cd is diametrical clearance: bushing inside diameter minus shaft diameter. Radial clearance is Cd/2. The calculator applies continuity to the exact concentric-annulus area.

Assumes a centered shaft, a uniform annulus, steady incompressible average flow, and enough differential pressure to produce the entered flow. This calculator does not determine the required differential pressure.

This calculator determines average fluid velocity through the annular opening between a pump shaft and a centered throat bushing. Enter any three of flush velocity, flow rate, diametrical clearance, and shaft diameter to calculate the fourth.

The formulas

Diametrical clearance is the difference between bushing inside diameter and shaft diameter, so Db = Ds + Cd. The exact annular area is A = π/4 · [(Ds + Cd)² − Ds²], and continuity gives Vf = Q/A. In US customary units this can be written directly as Vf (ft/s) = 0.4085 · Q (gpm) / [(Ds + Cd)² − Ds²] when both diameters are in inches.

Diametrical versus radial clearance

Cd is diametrical clearance, not the gap on one side. For a centered shaft, the radial gap is Cd/2. Entering radial clearance as Cd doubles the intended annular gap and produces the wrong area and velocity.

Solve in any direction

  • Flush velocity (Vf) — flow rate divided by the exact annular area.
  • Flow rate (Q) — annular area multiplied by the required average velocity.
  • Diametrical clearance (Cd) — the bushing-to-shaft diameter difference needed to provide the required area.
  • Shaft diameter (Ds) — the positive shaft diameter compatible with the specified area and clearance.

What the result represents

The result is bulk average axial velocity, based on total flow divided by open annular area. It does not describe the local velocity profile and does not calculate pressure drop, leakage behavior, or the differential pressure required to establish the entered flow. Confirm separately that the system has sufficient differential pressure and that the flow is appropriate for the pumped fluid and equipment.

Assumptions

  1. The throat bushing is centered around the shaft, creating a uniform concentric annulus.
  2. Enough differential pressure exists across the bushing to generate the required flow.
  3. Flow is steady and incompressible, and all dimensions describe the same operating geometry.

Worked example

For a 2.000 in shaft, 0.0625 in diametrical clearance, and 5 gpm flow, the bushing inside diameter is 2.0625 in and the annular area is 0.19942 in². The average flush velocity is 8.044 ft/s (2.452 m/s).

Variables

Symbol Meaning US unit SI unit
Vf Average flush velocity through the annulus ft/s m/s
Q Volumetric flow rate through the bushing gpm m3/h
Cd Diametrical clearance (bushing ID minus shaft diameter) in mm
Ds Shaft diameter in mm

Related calculators

Standards referenced

Continuity relation (Q = A × V) concentric-annulus geometry NIST SP 811 unit definitions and conversions

Verified Constants and formula two-source checked (PumpCalcs engineering review, 2026-08-25).

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