Fluid Properties and Statics
Key Takeaways
- Fluid mechanics is the highest-weighted topic on the FE Other Disciplines exam (12-18 questions, ~14%).
- Density ρ = m/V, specific weight γ = ρg, specific gravity SG = ρ/ρwater.
- Viscosity measures resistance to shear: dynamic viscosity μ (Pa·s), kinematic viscosity ν = μ/ρ (m²/s).
- Hydrostatic pressure increases linearly with depth: P = P₀ + ρgh (or P = P₀ + γh).
- Hydrostatic force on a submerged surface: F = γh̄A, where h̄ is the depth of the centroid.
- Buoyancy: an object in a fluid experiences an upward force equal to the weight of displaced fluid (Archimedes' principle).
Fluid Properties and Statics
FE Exam Weight: Fluid Mechanics accounts for 12-18 questions (~14%) — the HIGHEST weighted topic on the FE Other Disciplines exam. Master this section for maximum impact.
Fluid Properties
| Property | Symbol | Definition | SI Units |
|---|---|---|---|
| Density | ρ | Mass per unit volume | kg/m³ |
| Specific Weight | γ | Weight per unit volume = ρg | N/m³ |
| Specific Gravity | SG | ρ/ρwater = γ/γwater | Dimensionless |
| Dynamic Viscosity | μ | Resistance to shear deformation | Pa·s (N·s/m²) |
| Kinematic Viscosity | ν | μ/ρ | m²/s |
| Surface Tension | σ | Force per unit length at liquid surface | N/m |
| Bulk Modulus | Ev | Resistance to compression = -V(dP/dV) | Pa |
Properties of Water (at 20°C)
| Property | Value |
|---|---|
| Density | 998 kg/m³ ≈ 1,000 kg/m³ |
| Specific weight | 9,790 N/m³ ≈ 9,810 N/m³ |
| Dynamic viscosity | 1.002 × 10⁻³ Pa·s |
| Kinematic viscosity | 1.004 × 10⁻⁶ m²/s |
Newtonian vs. Non-Newtonian Fluids
Newton's Law of Viscosity:
| Fluid Type | Behavior | Examples |
|---|---|---|
| Newtonian | τ linearly proportional to du/dy | Water, air, oils |
| Shear-thinning | Viscosity decreases with shear rate | Ketchup, blood, paint |
| Shear-thickening | Viscosity increases with shear rate | Cornstarch + water |
| Bingham plastic | Requires yield stress to flow | Toothpaste, concrete |
Hydrostatic Pressure
where:
- P₀ = surface pressure
- h = depth below the surface
- ρ = fluid density
- γ = specific weight
Key Points:
- Pressure acts equally in all directions at a point (Pascal's law)
- Pressure increases linearly with depth for incompressible fluids
- Pressure is the same at all points on a horizontal plane in a connected fluid
- Gauge pressure = absolute pressure - atmospheric pressure
Manometers
For a U-tube manometer connecting fluid systems:
Work from one end to the other, adding pressure going down and subtracting going up.
Hydrostatic Forces on Surfaces
On a Plane Surface
Magnitude of resultant force:
where h̄ = depth of the centroid of the surface.
Location (center of pressure):
The center of pressure is always below the centroid (for non-horizontal surfaces).
On a Curved Surface
Resolve into horizontal and vertical components:
- Horizontal component = force on the vertical projection of the curved surface
- Vertical component = weight of the fluid above (or missing above) the curved surface
Buoyancy (Archimedes' Principle)
The buoyant force equals the weight of the fluid displaced by the submerged (or partially submerged) object.
Floating object: Buoyant force = weight of object → ρobject/ρfluid = fraction submerged
Stability of floating objects: Stable when the metacenter is above the center of gravity.
What is the gauge pressure at a depth of 10 m in water (ρ = 1,000 kg/m³)?
A rectangular gate is 2 m wide and 3 m tall, with its top edge 1 m below the water surface. What is the total hydrostatic force on the gate?
An object with SG = 0.8 floats in water. What fraction of its volume is submerged?