CELE Hydraulics & Fluid Mechanics — Hydrostatic Pressure and Forces on SurfacesConcept Map

Concept

Pressure Variation with Depth

Sub Concepts

• Gauge pressure (p = γh)
• Absolute pressure
• Atmospheric pressure
• Pressure head
• Pascal's Law
• Fluid properties (unit weight γ)

Relationship To Central

Foundational principle that pressure increases linearly with depth; basis for all hydrostatic force calculations

Concept

Manometry

Sub Concepts

• Simple manometers
• Differential manometers
• Mercury columns
• Inclined manometers
• Gauge fluid selection
• Walking the tube method

Relationship To Central

Practical measurement technique for determining pressure differences in fluid systems; validates theoretical pressure calculations

Concept

Force on Plane Surfaces

Sub Concepts

• Total force magnitude (F = γh̄A)
• Centroid depth calculation
• Center of pressure (yₚ = ȳ + Iₘ/(ȳA))
• Moment of inertia about centroidal axis
• Vertical plane surfaces
• Inclined plane surfaces
• Surface-piercing gates

Relationship To Central

Core topic for rectangular/inclined gates and walls; determines total force magnitude and location

Concept

Force on Curved Surfaces

Sub Concepts

• Horizontal component (FH = γh̄Avert)
• Vertical component (FV = γV)
• Circular arc gates
• Radial pressure distribution
• Resultant force direction
• Center of curvature pressure path

Relationship To Central

Extension to non-planar geometries; requires component resolution for practical design

Concept

Applications in Civil Engineering

Sub Concepts

• Spillway gates
• Radial gates
• Reservoir dams
• Water tanks
• Lock gates
• Canal gates
• Check dams
• Cofferdam design

Relationship To Central

Real-world implementations requiring hydrostatic force analysis for design and safety

Concept

Design Calculations and Procedures

Sub Concepts

• Problem identification
• Free body diagram setup
• Pressure distribution sketching
• Force magnitude computation
• Center of pressure location
• Moment and stability analysis
• Factor of safety determination

Relationship To Central

Systematic approach to solving hydrostatic force problems in engineering practice

To

Force on Plane Surfaces

From

Pressure Variation with Depth

Strength

strong

Relationship

Linear pressure variation (p = γh) is the foundation for calculating total force magnitude using F = γh̄A; the centroid depth h̄ replaces depth h because the pressure is not uniform across the surface

To

Manometry

From

Pressure Variation with Depth

Strength

strong

Relationship

Manometers apply the pressure-depth relationship to measure pressure differences by balancing fluid columns of known heights and specific weights

To

Center of Pressure

From

Force on Plane Surfaces

Strength

strong

Relationship

The total hydrostatic force acts not at the centroid but at the center of pressure yₚ = ȳ + Iₘ/(ȳA), which is always below the centroid due to the distribution of pressure increasing with depth

To

Force on Curved Surfaces

From

Force on Plane Surfaces

Strength

strong

Relationship

The horizontal component of force on a curved surface is calculated using the same plane surface method: FH = γh̄Avert, treating the vertical projection as a plane problem

To

Force on Curved Surfaces

From

Center of Pressure

Strength

moderate

Relationship

For curved surfaces, the center of pressure for the horizontal component is found using plane surface methods; for circular arcs, the resultant passes through the center of curvature

To

Center of Pressure

From

Moment of Inertia Calculations

Strength

strong

Relationship

The moment of inertia (Iₘ) of the surface area is essential for calculating center of pressure location; different shapes have different formulas requiring geometric knowledge

To

Engineering Applications

From

Force on Plane Surfaces

Strength

strong

Relationship

Hydrostatic force calculations on plane surfaces are directly applied to design vertical spillway gates, lock gates, dam faces, and tank walls

To

Engineering Applications

From

Force on Curved Surfaces

Strength

strong

Relationship

Curved surface analysis is applied to radial gates, Tainter gates, and cylindrical dam sections common in Philippine water resource projects

To

Pressure Variation with Depth

From

Manometry

Strength

moderate

Relationship

Manometer readings validate the theoretical pressure-depth relationship and allow field verification of pressure calculations in engineering practice

To

Force on Plane Surfaces

From

Design Process

Strength

strong

Relationship

The systematic design procedure starts with force magnitude calculation using F = γh̄A and includes determination of center of pressure for moment and stability analysis

To

Force on Curved Surfaces

From

Design Process

Strength

strong

Relationship

Design of curved gates requires component resolution into horizontal and vertical forces, followed by resultant magnitude and direction determination for structural analysis

To

Center of Pressure

From

Inclined Plane Surfaces

Strength

strong

Relationship

On inclined planes, ȳ is measured along the plane surface, h̄ = ȳ sin θ gives the vertical depth, and center of pressure is located along the plane using yₚ = ȳ + Iₘ/(ȳA)

To

Force on Curved Surfaces

From

Vertical Component of Force

Strength

strong

Relationship

The vertical component equals the weight of fluid directly above the curved surface (real or imaginary); critical for dams and gates where buoyancy effects occur

To

Force Calculations

From

Gauge Pressure

Strength

strong

Relationship

All hydrostatic force calculations use gauge pressure (pressure above atmospheric); absolute pressure is not directly used in force formulas for submerged surfaces

To

Force Magnitude

From

Centroid Calculation

Strength

strong

Relationship

The centroid location determines h̄, which directly multiplies by A to give total force; incorrect centroid location produces incorrect force magnitude