Mine Water Settling Calculations

Conical Settler Volume Calculation

• Volume of a conical settler can be derived using the formula: ( V = \frac{1}{3} \pi r^2 h ), where ( r ) is the radius and ( h ) is the height of the cone.
• Effective settling volume is influenced by the reduced volumes of connected settlers:
  • Settler A reduced by 40%
  • Settler B reduced by 25%
  • Settler C reduced by 10%

Displacement Rock Cavity Size

• Size of the displacement rock cavity depends on the flow of mine water at a rate of 200 m³/hr.
• For settling 50µ particles and water with specific gravity of 0.8, calculate volume using Stokes' law for settling particles.
• With 90% efficiency, use the equation relating the volume flow rate to the cavity dimensions to determine diameter of the circular cavity.

Sump Location Factors

• Consideration of surrounding geology and hydrology to prevent flooding.
• Accessibility for maintenance and emergency evacuations.
• Location relative to the site of water collection and transportation needs.

Masonry Dam Load Analysis

• The load on a masonry dam is determined using hydrostatic pressure formula: ( P = \gamma h ), where ( \gamma ) is specific weight of water (approximately 9.81 kN/m³).
• For an arc of a circle with radius 30m subtending an angle of 60°, calculate load in N/m length at different heights.
• The position of the line of action can be found by determining the center of pressure, leveraging geometric relationships within the arc.

Bridge Arch Calculations

• The upward force on the underside of a semi-circular arch can be analyzed using hydrostatic pressure: ( F = \gamma V ).
• For bridge arch width of 4m and 1.25m water above crest, compute the vertical forces acting on the structure.
• Analyze horizontal thrust using principles of equilibrium and geometry specific to arches.

Fluid Flow and Energy Equation

• Energy equation between two points in a frictionless pipe includes terms for potential energy (height), pressure energy, and kinetic energy: ( \frac{P_1}{\gamma} + z_1 + \frac{v_1^2}{2g} = \frac{P_2}{\gamma} + z_2 + \frac{v_2^2}{2g} ).
• Assumptions of Bernoulli's equation include:
  • Steady flow
  • Incompressible fluid
  • No friction losses
• Use given parameters to calculate discharge at B and the energy loss due to friction between points A and B, considering height differences and pressure heads.