Fluid Properties and Hydrostatics

What is a Fluid?

A fluid is any substance that deforms continuously under applied shear stress. Both liquids and gases are fluids.

Key Fluid Properties

Density (ρ)

• ρ = mass/volume
• Water: 1000 kg/m³ = 62.4 lb/ft³
• Air (STP): 1.225 kg/m³

Specific Weight (γ)

• γ = ρg
• Water: γ = 9810 N/m³ = 62.4 lb/ft³

Specific Gravity (SG)

• SG = ρ_fluid / ρ_water
• Dimensionless

Dynamic Viscosity (μ)

• Resistance to shear deformation
• Units: Pa·s (N·s/m²) or lb·s/ft²
• Water at 20°C: μ = 0.001 Pa·s

Kinematic Viscosity (ν)

• ν = μ/ρ
• Units: m²/s or ft²/s

Pressure in Static Fluids

Pressure increases with depth:

P = P₀ + ρgh

• P₀ = surface pressure (often atmospheric = 101.3 kPa)
• ρ = fluid density
• g = 9.81 m/s²
• h = depth below surface

Gauge vs. Absolute Pressure

• P_abs = P_gauge + P_atm
• Gauge pressure is measured relative to atmosphere

Hydrostatic Force on Submerged Surfaces

For a horizontal surface: F = γ × h × A

For an inclined surface:

• F = γ × h_c × A (where h_c is depth to centroid)
• Center of pressure is below centroid

Pascal's Law

Pressure applied to an enclosed fluid is transmitted equally in all directions → basis of hydraulic systems.

Archimedes' Principle

Buoyant Force = weight of fluid displaced

F_b = γ_fluid × V_submerged

Summary

Understand fluid properties before moving to flow. Hydrostatic pressure, buoyancy, and force on surfaces are fundamental to dam design, tank design, and hydraulics.