Skip to main content

Sediment Settling Velocity Rubey Formula Calculator

The terminal fall velocity of sediment particles in water governs sedimentation basin design, bedload transport, and dredging mechanics.

Median sieve grain diameter of sediment particle (e.g. 0.2 mm fine sand to 5.0 mm gravel).

Specific gravity of sediment material (typically 2.65 for natural quartz sand).

Water temperature governing dynamic fluid viscosity and density.

Calculated Result
0.0924 m/s

Fall / Settling Velocity (wₛ)

Settling Velocity (cm/s)

9.24 cm/s

Particle Reynolds Number

45.56

Stokes Theoretical Velocity

0.2217 m/s

Hydrodynamic Flow Regime

Transitional (Rubey intermediate zone, medium/coarse sand)

Calculation Breakdown

  1. Kinematic Viscosity (ν)ν = 0.000001014 m²/s at 20 °C
  2. Rubey Settling Formulationw_s = [√((4/3) g (s - 1) d³ + 36 ν²) - 6 ν] / d = 0.0924 m/s (9.24 cm/s)
  3. Particle Reynolds Number (Re_p)Re_p = (w_s · d) / ν = 45.56 (Transitional (Rubey intermediate zone, medium/coarse sand))

Sediment Hydrodynamic Metrics

Interactive visualization based on your current inputs

Value
0.08.4172534Fall Velocity (cm/s)Stokes Velocity (cm/s)Re_pDiameter (mm x 10)ParameterValue

What Is the Sediment Settling Velocity Rubey Formula Calculator?

The terminal fall velocity of sediment particles in water governs sedimentation basin design, bedload transport, and dredging mechanics.

While fine particles obey Stokes’ law and large gravel obeys Newton’s quadratic drag law, natural sands fall into the intermediate transitional regime.

This calculator computes water kinematic viscosity as a function of temperature and evaluates Rubey’s universal formulation across all hydrodynamic regimes.

How Does the Sediment Settling Velocity Rubey Formula Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Sediment Settling Velocity Rubey Formula Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

w_s = \frac{\sqrt{\frac{4}{3} g (s - 1) d^3 + 36 \nu^2} - 6\nu}{d}, \quad Re_p = \frac{w_s \, d}{\nu}

ws is terminal settling velocity, g is gravity, s is specific gravity (rho_s/rho_w), d is particle diameter, and nu is water kinematic viscosity.

How to Use the Sediment Settling Velocity Rubey Formula Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

Medium Quartz Sand in River Water

Input Values:

grainDiameterMm:0.5
particleSpecificGravity:2.65
waterTemperatureCelsius:20
Worked Steps: Determines settling velocity ws = 0.068 m/s (6.8 cm/s) in transitional regime.

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Rubey (1933) formulation provides a continuous analytical function from Stokes laminar to Newton turbulent drag.
  • Water kinematic viscosity ν is calculated via Poiseuille’s temperature approximation.
  • Particle Reynolds number Re_p classifies the hydrodynamic regime (laminar, transitional, or turbulent).

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

Explore more tools and calculators in Math Calculators