Fundamental Fluid Mechanics Concepts and Definitions

Posted on Mar 31, 2025 in Geology

Pascal’s Principle

When pressure is exerted on a liquid in equilibrium, this pressure is transmitted equally to all molecules throughout the fluid.

Turbulent Flow Regime

Characterized by unequal particle movement, where particles collide with each other and against the walls of the conductive element, bouncing off and losing energy.

Full Contraction in a Hole

Liquid streams (fillets) occupy the periphery of a hole and come close to the interior zones. They slide along the walls and have a very strong curvature upon exiting. This causes the liquid vein to have a real drainage section smaller than the total hole area.

Reynolds Number

A dimensionless parameter related to fluid characteristics. It defines the relationship between inertial forces and viscous forces within the fluid flow.

Hydraulic Machine

A machine that provides specific energy to a fluid (like a pump) or subtracts energy from it (like a turbine).

Liquid Streamline (Fillet)

The trajectory followed by moving liquid particles. It represents the path formed as particles pass one by one through a specific point over time.

Pipe Roughness

The quotient between its absolute roughness (ka) and the inner diameter (D). Relative Roughness = ka / D.

Cavitation

A phenomenon that occurs whenever the pressure at some point or zone within a liquid stream drops below a minimum admissible value (vapor pressure). This can happen in hydraulic structures and machines, potentially causing metal destruction.

Flow Rate (Q)

The volume of fluid passing through a cross-section of the stream per unit of time. Q = V · S (where V is velocity and S is cross-sectional area).

Specific Gravity (γ)

Weight per unit volume. It is a function of temperature (t) and pressure, although pressure variation has little effect on liquids. γ = Weight / Volume = (m · g) / V = ρ · g (where m is mass, g is gravity, V is volume, ρ is density).

Pressure (P)

The relationship between force (F) and the surface area (S) it acts upon (P = F/S). Absolute Pressure (Pabs) = Manometric Pressure (Pman) + Atmospheric Pressure (Patmos).

Dynamic Viscosity (μ)

In real liquids, cohesive forces between molecules and adhesive forces between molecules and the conduit walls cause friction as particles move. This internal friction coefficient of the fluid is called dynamic viscosity (μ).

Kinematic Viscosity (ν)

The relationship between dynamic viscosity (μ) and density (ρ). ν = μ / ρ. Common unit: Stoke (St).

Shear Stress (τ)

Also known as tangential stress. In these stresses, the force acts parallel to the area, causing the fluid to deform continuously.

Surface Tension (σ)

Tension occurring at the surface of liquids, where the liquid comes into contact with another fluid (like gas). Explanation: A molecule within the bulk liquid is in equilibrium due to surrounding forces. However, a molecule at the surface experiences a net inward force (attraction towards the liquid) because there are fewer attracting liquid molecules above it compared to below and beside it. This results in a force perpendicular to the surface, directed inwards.

Power (P)

Work done per unit of time.

Permanent and Uniform Flow

Flow is permanent (steady) at a point when the velocity does not change with time. Flow is uniform if the movement conditions (e.g., velocity, depth) are the same in all normal cross-sections along the flow path.

Discrete Distribution Pipes

A pipe, typically made of a single material with a uniform internal diameter, equipped with emitters (e.g., drippers, sprinklers) spaced equidistantly. The distance between the first emitter and the origin may differ. These emitters discharge flow along the pipe’s length. Consequently, the initial flow rate (Qorigin) decreases along the pipe, potentially reaching zero at the end.

Factors Influencing Suction Lift Height

  • Water Density: Impurities like sand, salt, or soil can increase water density, which decreases the maximum suction height.
  • Elevation: At higher altitudes above sea level, atmospheric pressure decreases. This reduced atmospheric pressure lowers the maximum achievable suction lift height.
  • Water Temperature: As water temperature increases, its vapor pressure rises. Water boils at lower pressures when hotter. Increased vapor pressure reduces the effective pressure difference available for suction, thus lowering the maximum suction lift height.

Water Hammer (Coup de Bélier)

A phenomenon occurring due to rapid changes in water circulation velocity (e.g., sudden valve closure). It causes pressure surges (positive and negative pressure waves) that dampen over time. It is a transient phenomenon involving variable velocity, non-rigid pipes, and compressible fluid behavior.

Dimensional Analysis

  • Kinematic Viscosity (ν): L2 T-1 (Standard Formula: ν = μ / ρ)
  • Dynamic Viscosity (μ): M L-1 T-1
  • Surface Tension (σ): M T-2 (Formula: σ = Force / Length)
  • Shear Stress (τ): M L-1 T-2 (Formula: τ = Force / Area)
  • Power (P): M L2 T-3 (Formula: P = Work / Time)
  • Momentum: M L T-1 (Formula: Momentum = Mass × Velocity)
  • Flow Rate (Q): L3 T-1 (Formula: Q = Volume / Time)
  • Specific Weight (γ): M L-2 T-2 (Formula: γ = Weight / Volume)
  • Pressure (P): M L-1 T-2 (Formula: P = Force / Area)