Fluid Mechanics Overview for Dredging

Important concepts water, sediment flow through pipes, losses due to friction in pipe systems.

Definitions of Fluid Mechanics Properties

 

  • ρ = mass/volume = fluid density
    • ρwater = 1.94 slugs/ft3 = 999 kg/3
    • ρseawater = 1.99 slugs/ft3 = 1030 kg/m3
  • g = length/time2 = acceleration due to gravity
    • g = 32.2 ft/s2; 9.81 m/22
  • y = weight/volume  = ρg = specific weight
    • y water = 62.4 lb/ft3; 9.8 kN/m3
    • y seawater = 64.0 lb/ft3; 10.1 kN/m3
  • SG = specific gravity = ρsubstance /ρwater @ 4° Celcius
    • SG SAE 30 = 0.91
    • SG water = 1.00
    • SG seawater = 1.03
    • SG HG = 13.61
    • SG slurry = 1.1 – 1.5
    • SG (solid) sand = 2.65
    • SG (loose) sand = 1.9 – 2.1
  • μ – dynamic viscosity
    • t = μ du/dy
  • ⋎ – kinematic viscosity
    • ⋎ = μ
  • Re – Reynolds Number inertia force / viscous force
    • Re = ρ D U/μ = U D/v    (pipe flow)
    • U – average velocity in pipe
    • D – pipe inside diameter

Reynolds Number (Re) for Pipe Flow

To determine if slurry flow is laminar or turbulent

  • Re < 2000    Laminar Flow
  • Re > 4000   Turbulent Flow

Example:

Slurry (1.2 Specific Gravity) flows at 15 ft/2 through a 24 inch inside diameter pipe.

Is the flow laminar or turbulent?

Re = (1.94 slugs/ft3(1.25)(15 ft/s)(24 in/12 ft)2.34E-5 lb s/ft2)
Re = 3,110,000
Flow is TURBULENT

Pressure Relationships

Dredging Fluid Dynamics Pressure Relationships

Pressure & Buoyancy

How pressure is quantified and buoyancy in individual sediment grains that are floating through your slurry. Buoyant force is equal to weight of the displaced fluid x by the specific weight of the displaced fluid. 

Archimedes law

Continuity Equation

Continuity Equation

Bernoulli Equation

Compare different contributions to energy flow in pipe systems.  Calculate flow rates, velocities, losses.

Bernoulli Equation

Energy Equation

Calculate Losses in Pipe Systems

Energy Equation

Friction Loss in Slurry Flow

Friction Loss Slurry Pipe

Moody Diagram – Friction in Slurry Flow

Moody chart diagram

The equation for Calculating Friction Factor (f)

Calculating Friction Factor in Slurry Flow through Slurry Pipelines

Relative Roughness of Slurry Pipelines Material

Relative Roughness of Slurry Pipeline

Equivalent Length of Pipe (losses)

Losses in Slurry Flow Pipes

Pump Input Energy

Pump Input Energy