Food Process Engineering & Operations

Bernoulli's equation expresses the total mechanical energy balance for frictionless, incompressible fluid flow along a streamline (sum of pressure energy, kinetic energy, and potential energy per unit mass is constant):

$$\frac{P}{\rho} + \frac{v^2}{2} + gz = \text{constant}$$

The continuity equation represents mass conservation, Fourier's law governs heat conduction, and Plank's equation models food freezing time.

Conversion calculation:
Given velocity $v = 5.47\text{ ft/s}$.
Since $1\text{ ft} = 0.3048\text{ m}$ and $1\text{ min} = 60\text{ seconds}$:

$$v = 5.47\text{ ft/s} \times 0.3048\text{ m/ft} \times 60\text{ s/min} = 5.47 \times 18.288 = 100.035\text{ m/min} \approx 100\text{ m/min}$$

Texture Profile Analysis (TPA) parameters:

• Springiness (originally called elasticity) is defined as the rate and extent to which a deformed material recovers toward its undeformed condition after the deforming compressive force is removed.
• Hardness is the peak force during the first compression bite.
• Cohesiveness is the ratio of the positive force area during the second compression to that during the first compression.

Transport phenomena and heat transfer principles:

• In heat exchangers (e.g., plate or scraped surface), convective heat transfer coefficient ($h$) is inversely proportional to fluid viscosity ($\mu$): $h \propto \mu^{-0.47}$ (Dittus-Boelter / Sieder-Tate correlation).
• As liquid food viscosity increases, the fluid moves more sluggishly (laminar regime, thicker boundary layer), dramatically diminishing turbulence and heat transfer efficiency.
• Total soluble solids and concentration are directly (positively) correlated with viscosity.