Fluid Properties and Pressure Dynamics

Richard Rhodes
- Background: Sculptor and stonemason, currently a visiting professor.
- Lecture Topic: Intersection of art and engineering, focusing on large projects.
- Lecture Style: General and engaging, not heavily focused on equations.
Recap of Previous Class: Focus on fluid properties (Slug Gamma).

Definition of Viscosity:
- Property of a fluid that resists motion.
- Higher viscosity means more effort is needed to make the fluid conform.
- Example: Honey and oil have higher viscosities than water.
Symbol Used: Greek letter mu (μ) represents dynamic or absolute viscosity.
Relationship to Shear Stress:
- Viscosity (μ) is the proportional constant between shear stress (τ) and velocity gradient (du/dy).
- $\tau = \mu \frac{du}{dy}$
- Shear stress induces motion along the fluid surface.
No Slip Boundary Condition:
- Fluid at the boundary moves at the same speed as the boundary itself.
- Velocity profile: Fastest at the moving plate, zero at the bottom wall.
Units of Viscosity:
- SI Units: Newton second per meter squared (N·s/m²).
- Traditional Units: Pound force second per foot squared (lb·s/ft²).
Kinematic Viscosity: Defined as $\nu = \frac{\mu}{\rho}$ , where ρ is fluid density.
- Units: m²/s.

Newtonian Fluids: Viscosity (μ) is constant, regardless of shear stress.
Non-Newtonian Fluids: Viscosity changes based on shear stress applied.
- Typically not covered in the course except possibly as homework references.
- Often depend on temperature, e.g., heating honey to reduce viscosity.

Homework due dates: Current homework due Thursday, new homework will be released today.
Challenge activities made optional to balance workload, but are beneficial for mastering the material.

Pressure Definition:
- Pressure (p) has units of N/m² or Pascals (Pa).
- In traditional units, often expressed in PSI (pound force per square inch).
Absolute vs Gauge Pressure:
- Absolute pressure: Measured relative to a perfect vacuum.
- Gauge pressure: Measured relative to atmospheric pressure.
- Gauge pressures can be negative, but absolute pressure cannot.

Hydrostatic Equation: $\frac{dP}{dz} = -\gamma$ , where
- γ is the specific weight of the fluid.
- Pressure decreases with height in a fluid at rest; with elevation, pressure decreases as weight of the fluid increases.
Examples:
- Water is generally incompressible and has a nearly constant specific weight.
- Air density changes with elevation, significantly affecting pressure calculations in the atmosphere.

Ideal Gas Law: Relates pressure (p), density (ρ), gas constant (R), and absolute temperature (T):
- $p = \rho RT$ .
Hydrostatic pressure changes can be derived using this relationship.

Function of Manometers: Measure pressure differences or pressures.
Monometer Equation: $p1 = p2 + \gamma h$ , where h is the height difference in fluid levels.
Assumptions:
- Pressure equal between two points at the same height is true only in the same fluid with equal specific weights.
- Weight of the air column can typically be neglected in most manometer calculations.

Given a manometer with two different fluids and associated heights (h1, h2) and specific weights (γ1, γ2), derive the pressure at point A (pA):
- $pA = p{atmosphere} + h2 \gamma2 - h1 \gamma1$ .

Pressure Forces: Magnitude calculated as pressure multiplied by area (F = pA).
Hydrostatic Force: Forces vary depending on the shape of the submerged plane.
- For a rectangular plane submerged, calculate varying pressures using integrals due to varying depths of the fluid columns.

Review the principle of calculating pressure forces acting on submerged surfaces where pressure increases with depth.
Introduction of more complex scenarios involving angled plates and curved surfaces in future classes.
Emphasis on practice and understanding the quantitative relationships in fluid mechanics through example problems and exercises.