Fluid Statics & Dynamics: Viscosity, Rheology of Dairy Fluids, Reynolds Number, Laminar vs Turbulent Flow & Bernoulli's Theorem

Dimensional derivation of dynamic viscosity:

• $\text{N}\cdot\text{s/m}$ is damping coefficient.
• From Newton's law of viscosity:
  $$\tau = \mu \frac{du}{dy} \implies \mu = \frac{\tau}{du/dy} = \frac{\text{N/m}^2}{(\text{m/s})/\text{m}} = \frac{\text{N/m}^2}{1/\text{s}} = \text{N}\cdot\text{s/m}^2$$
  This is equivalent to the Pascal-second ($\text{Pa}\cdot\text{s}$ or $\text{kg}/(\text{m}\cdot\text{s})$), the standard SI unit of dynamic viscosity.
• $\text{N/s}$ is rate of force change.
• $\text{N}\cdot\text{m}$ is torque or Joule (work/energy).

Working principles of flowmeters vs pressure measuring instruments:

• An Orificemeter measures flow rate by creating a differential pressure across a constriction based directly on Bernoulli's principle.
• Venturimeter accelerates fluid through a converging-diverging throat to convert pressure head to velocity head per Bernoulli's equation.
• Pitot tube measures fluid velocity by converting kinetic energy into stagnation pressure head per Bernoulli's equation.
• Bourdon tube is a mechanical pressure gauge that operates based on the elastic mechanical deflection/uncoiling of a flattened, curved metal tube subjected to internal static fluid pressure; it does not utilize fluid velocity or Bernoulli's hydrodynamic energy equation.

Fundamental laws of hydrostatics:

• Archimedes' principle governs buoyant upward force on submerged bodies.
• Bernoulli's principle relates pressure, velocity, and elevation along a streamline in moving fluids.
• Pascal's Law states that in a fluid at rest in a closed system, the pressure exerted at any point is transmitted equally and undiminished in all directions throughout the fluid ($P_x = P_y = P_z$).
• Continuity principle governs mass conservation in fluid conduits ($A_1 v_1 = A_2 v_2$).