Fluid Mechanics Overview - Slurry Pumping and Dredge Consulting

Definitions
Pressure & Buoyancy
Continuity Equation
Bernoulli Equation
Energy Equation (Modified Bernoulli)

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/ρ
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

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.