CIVE 210: Hydraulics - Fluid Flow & Dimensional Analysis

Vocabulary flashcards for fluid flow and dimensional analysis concepts.

Fluid

A material that cannot sustain a shearing stress in the absence of motion

Viscosity

Physical property that determines the ease with which a fluid will flow

Fluid viscosity

Ratio of shear stress to shear rate; measure of a fluid's resistance to flow.

Dynamic viscosity (𝜇)

𝜇 = shear stress/ shear rate (N•s/m2)

Viscosity

Shear stress (𝜏) divided by shear rate (Γ)

Newtonian fluid

Fluids for which shear stress is directly proportional to shear rate

Non-Newtonian fluid

A fluid that does not follow Newton's law of viscosity, where viscosity changes under applied force.

Kinematic viscosity (𝜈)

kinematic viscosity = dynamic viscosity/ density (m2/s)

Physical process

a set of variables 𝑷 = 𝒇(𝒙𝟏, 𝒙𝟐, … , 𝒙𝒏) which have dimensions (length 𝐿, mass 𝑀, time 𝑇) and are measured in units

Dimensional homogeneity

Each side of an equation must have the same dimensions

Dimensional analysis

If the 𝑛 variables have 𝑑 dimensions, the variables can be combined into 𝐺 = 𝑛 − 𝑑 dimensionless groups

Buckingham 𝝅 theorem

If the 𝑛 variables have 𝑑 dimensions, the variables can be combined into 𝐺 = 𝑛 − 𝑑 dimensionless groups

Rayleigh method

use dimensional homogeneity to find 𝒙𝒏, 𝒚𝒏, 𝒛𝒏

𝝅𝟐

Δ𝑝 𝜌𝑉^2

𝝅𝟑

𝑙/𝐷

𝝅𝟔

𝜇/𝜌𝑉𝐷

𝝅𝟖

𝜖/𝐷

Reynolds number (𝑹𝒆)

𝑉𝐷/𝝂

Relative roughness

𝜖/𝐷

Friction factor (f)

measure of frictional losses in a pipe , 𝟐(Δ𝑝/𝜌𝑉^2)(𝐷/L)

Meaning of Re

Fluid exerts a force on the wall and wall exerts an equal and opposite force on the fluid

Critical velocity

velocity at which the flow change from laminar to turbulent or vice versa.

Lower critical velocity

velocity at which the flow change from laminar to turbulent (Transitional).

Upper (or higher) critical velocity

velocity at which the flow change from turbulent to laminar (Transitional).

Relative roughness

Absolute roughness/Diameter