Fluid Mechanics - Exam 1 Vocab - ERE 339

Fluid

• Formal: A substance that deforms continuously under any applied shear stress, no matter how small.

• Layman: Solids resist shape change; fluids (liquids, gases) just “flow” when you push sideways.

• Example: A cube of Jell-O can resist shear (so it’s a solid), but water cannot — it moves immediately.

Viscosity

• Formal: The property of a fluid that quantifies resistance to shear deformation (internal friction).

• Layman: Thickness or “gooiness” of a fluid.

• Example: Honey has higher viscosity than water — it flows slower when you tip a jar

Dynamic vs. Kinematic Viscosity

• Dynamic (μ): Ratio of shear stress to velocity gradient, units: Pa·s = N·s/m².

• Kinematic (ν): Ratio of dynamic viscosity to density, ν = μ/ρ, units: m²/s.

• Layman: μ tells you how “sticky” the fluid is; ν tells you how “sticky it is relative to how heavy it is.”

• Example: Oil and water may have similar μ, but water is less dense → different ν.

Boundary Layer & No-Slip Condition

• Boundary layer (BL): Region near a solid surface where velocity changes from 0 at wall (no slip) to free stream value.

• No-slip condition: Fluid velocity at a solid surface = velocity of the surface.

• Layman: The layer of air sticking to a car window that slows down → drag comes from that.

• Example: Paint on a wall → dust sticks to the thin BL

Surface Tension, Cohesion vs. Adhesion, Contact Angle

• Surface tension (γ): Force per unit length (N/m) at a liquid–air interface, due to cohesive molecular forces.

• Cohesion: Attraction between like molecules (water to water).

• Adhesion: Attraction between unlike molecules (water to glass).

• Contact angle (θ): Angle between liquid surface and solid wall → indicates wetting.

• Layman: Water beads up on wax paper (cohesion > adhesion, θ > 90°). Water climbs glass (adhesion > cohesion, θ < 90°).

Capillary Rise & Bond Number

• Equation:h=2γcos⁡θ/(ρgr)

• Bond number (Bo): Ratio of gravity to surface tension forces: Bo=(ρgr²)/γ.

• Layman: Tiny tube → water climbs up because surface tension beats gravity. Big tube → gravity wins, no climb.

Hydrostatics: Pressure vs. Depth

• Formal: p=p_o+ρgh Pressure increases linearly with depth, independent of container shape.

• Layman: A tall skinny tank and a wide tank of same depth both exert same pressure at bottom.

Buoyancy

• Formal: Upward force on a body in a fluid = weight of displaced fluid (Archimedes’ principle).

• Layman: If you push an object in water, it “weighs less” because water pushes up.

• Example: A boat floats because water’s upward push balances its weight

Absolute vs. Gauge Pressure

• Absolute: Pressure measured relative to a vacuum.

• Gauge: Pressure measured relative to atmospheric pressure.

• Layman: Tire gauge reads 32 psi gauge; actual absolute pressure inside tire ≈ 32 + 14.7 = 46.7 psi

Force Balance vs. Moment Balance

• Force balance: ∑F=0. Net forces cancel (static equilibrium).

• Moment balance: ∑M=0. No net torque → no tipping/rotation.

• Layman: Standing up: your weight pushes down, the floor pushes up (force balance). If you lean too far, moments don’t balance → you tip

Hydrostatic Resultant Force vs. Center of Pressure

• Resultant force (F): Total force from pressure distribution: F=ρgAh_c

• Center of pressure (y_cp): Depth where resultant acts: h_c+ (I_g/Ah_c ). Always below centroid.

• Layman: Push on a door underwater → force is not evenly spread; it acts deeper than halfway

Shear stress (τ)

Force per unit area parallel to surface, τ=μdv/dy