Unit 8: Fluids

You’ll explore the behavior and motion of materials that can change shape and analyze how that behavior interacts with other objects.

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8.1 Internal Structure and Density

Fluids include liquids and gases—they flow and take the shape of their container.

Density (ρ) is mass per unit volume:

ρ = m/V

• Fluid Properties:

  • Liquids have definite volume but no fixed shape.

  • Gases have neither definite volume nor fixed shape.

  • Viscosity measures a fluid’s resistance to flow (e.g., honey = high viscosity, water = low).

  • Compressibility describes how much a fluid's volume changes under pressure.

• Factors influencing fluid behavior include:

  • Temperature

  • Pressure

  • Dissolved substances or suspended particles

8.2 Pressure

Pressure (P) is force per unit area:

P = F/A

• Measured in pascals (Pa), where 1 Pa = 1 N/m².

Hydrostatic Pressure:

P = ρgh 

• Increases with depth h

• g = 9.8 m/s² (acceleration due to gravity)

Types of Pressure

• Gauge pressure: pressure above atmospheric pressure.

• Absolute pressure: gauge pressure + atmospheric pressure.

• Pressure is the same in all directions at a given depth (Pascal’s Principle).

Measurement

• Manometers and pressure gauges are used to measure fluid pressure.

• Hydrostatic pressure sensors use Pascal’s Principle for operation.

8.3 Fluids and Newton's Laws

Buoyancy and Archimedes' Principle

• Buoyancy is the upward force a fluid exerts on a submerged object.

• Archimedes’ Principle:
  The buoyant force F_b​ is equal to the weight of displaced fluid:

F_b​ = pgV

• Floating or Sinking:

  • Float: Weight < Buoyant Force

  • Sink: Weight > Buoyant Force

  • Neutral: Weight = Buoyant Force

• Apparent weight is reduced in a fluid due to buoyant force.

• Center of buoyancy: Point where buoyant force acts (center of displaced fluid volume).

Pascal’s Principle and Hydraulics

• States that pressure applied to a confined fluid is transmitted undiminished throughout.

• Force multiplication in hydraulics:

Hydraulic systems:

• Use incompressible fluids (e.g., oil)

• Used in car brakes, hydraulic lifts, heavy machinery
  Pressure remains constant through the system

8.4 Fluids and Conservation Laws

Fluid Dynamics and Flow

• Fluid dynamics studies motion of fluids and includes:

  • Velocity, flow rate, viscosity

• Laminar flow: Smooth, orderly flow in layers

• Turbulent flow: Chaotic, irregular flow

Continuity Equation (Conservation of Mass):

ρ₁A₁v₁ = ρ₂A₂v₂

• Describes how the flow rate is constant in steady flow

Bernoulli’s Principle (Conservation of Energy in Fluids):

• When velocity increases, pressure decreases (and vice versa)

P + 1/2pv² + pgh = constant

Reynolds Number:

• Dimensionless number used to predict flow type (laminar vs. turbulent)

Ideal Gas Law (Conservation of Mass & Energy for Gases):

PV = nRT

• Relates pressure, volume, temperature, and number of moles in a gas