๐ Lesson 6
D4
Hydrostatic Pressure Distribution and Manometry
Hydrostatic pressure is the force that water or other fluids exert due to their weight when theyโre not moving.
๐ฏ Learning Objectives
- โ Calculate hydrostatic pressure at any depth in a homogeneous fluid using ฯgh
- โ Analyze pressure distribution across submerged mine structures (e.g., bulkheads, sump walls) to assess structural loading
- โ Apply manometric principles to interpret gauge and absolute pressures from U-tube and inclined manometers used in mine water monitoring
- โ Design a simple piezometer system for groundwater pressure measurement in an open-pit slope
๐ Why This Matters
In underground and open-pit mining, hydrostatic pressure governs water inflow into excavations, stability of flooded stopes, design of dewatering systems, and safety of tailings dam instrumentation. Misjudging fluid pressure can lead to catastrophic bulkhead failure, uncontrolled inflows, or erroneous pore-pressure readings in slope stability analyses โ all directly impacting worker safety and operational continuity.
๐ Core Principles
Fluid statics begins with the fundamental assumption that a static fluid cannot sustain shear stress โ thus, pressure acts equally in all directions (Pascalโs Law). Pressure variation with depth follows from force balance on a fluid element: dP/dz = โฯg (with z positive upward). Integrating yields P = Pโ + ฯgh, where h is depth below the free surface. For layered fluids or manometers, pressure continuity across interfaces and density-weighted height differences must be respected. Gauge pressure excludes atmospheric contribution; absolute pressure includes it (P_abs = P_gauge + P_atm).
๐ Hydrostatic Pressure Equation
The basic hydrostatic pressure equation relates pressure to depth, fluid density, and gravity. It applies to incompressible, homogeneous, static fluids โ a valid assumption for mine water, slurries (at rest), and oil-based manometric fluids.
Hydrostatic Pressure (Gauge)
P = ฯghComputes gauge pressure at depth h in a static, incompressible fluid.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| P | Gauge pressure | Pa (N/mยฒ) | Pressure relative to local atmospheric pressure |
| ฯ | Fluid density | kg/mยณ | Mass per unit volume of the static fluid |
| g | Gravitational acceleration | m/sยฒ | Local acceleration due to gravity (typically 9.78โ9.83 m/sยฒ at mining latitudes) |
| h | Depth below free surface | m | Vertical distance from fluid surface to measurement point |
Typical Ranges:
Mine sump water: 10โ150 kPa (1โ15 m depth)
Tailings pond interface: 50โ300 kPa (5โ30 m slurry depth)
๐ก Worked Example
Problem: A dewatering sump in an underground mine contains water (ฯ = 1000 kg/mยณ) to a depth of 8.5 m. The local gravity is 9.78 m/sยฒ. Atmospheric pressure is 101.3 kPa. Calculate (a) gauge pressure at the sump floor, and (b) absolute pressure.
1.
Step 1: Identify knowns โ ฯ = 1000 kg/mยณ, g = 9.78 m/sยฒ, h = 8.5 m
2.
Step 2: Apply P_gauge = ฯgh = (1000)(9.78)(8.5) = 83,130 Pa = 83.1 kPa
3.
Step 3: Compute P_abs = P_gauge + P_atm = 83.1 + 101.3 = 184.4 kPa
Answer:
The gauge pressure is 83.1 kPa, and absolute pressure is 184.4 kPa โ both within safe operating limits for standard HDPE sump liners rated to โฅ200 kPa.
๐๏ธ Real-World Application
At the Bingham Canyon Mine (Utah, USA), hydrostatic pressure calculations guided the redesign of the North Wall Piezometer Network following accelerated pore-pressure rise during heavy rainfall. Engineers used ฯgh-based calibration of vibrating-wire piezometers to distinguish between artesian groundwater pressure and barometric effects, enabling real-time slope stability assessment per SME Guidelines for Groundwater Monitoring in Open Pit Mines (2021).
โ๏ธ Student Exercise
A mercury (ฯ_Hg = 13,600 kg/mยณ) manometer is connected to a pressurized water pipe in a mill sump. The mercury column shows a 24 cm height difference, with mercury higher on the side open to atmosphere. Calculate the gauge pressure in the water pipe. Assume g = 9.81 m/sยฒ.
๐ง Interactive Calculator
๐ง Open Fluid Flow and Transport Phenomena Calculator๐ Case Connection
๐ Cooling Water Circuit Fouling Mitigation in Refinery FCC Unit
Biofilm + CaCOโ scaling reduced heat transfer by 38%, risking catalyst deactivation
๐ Pneumatic Conveying of Catalyst Powder in Fluidized Bed Reactor Feed System
Catalyst attrition and line plugging due to intermittent slug flow and particle segregation