Fluids

Phases of Matter

The phases of matter are distinguished by their physical properties, such as shape, volume, and ability to flow. Understanding these phases is essential for studying fluid mechanics in physics.

• Solid: Maintains shape and volume; requires significant force to change shape; atoms are fixed in place.

• Liquid: Takes the shape of its container; maintains a fixed volume; can flow; atoms are less tightly bound than in solids.

• Gas: No fixed shape or volume; fills the container; can flow and compress easily; atoms are widely separated.

• Plasma: Ionized atoms; found in stars; not typically covered in classical physics courses.

Special Cases: Amorphous solids (e.g., glass) technically flow very slowly; some biological materials and LCD TVs exhibit properties between solids and fluids.

Additional info: Some phases (marked with *) require advanced physics to fully describe.

Fluid Properties and Density

Fluids are characterized by their ability to flow and conform to the shape of their container. Key properties include density, area density, and linear density.

• Density (ρ): Mass per unit volume.

• Area Density (σ): Mass per unit area.

• Linear Density (μ): Mass per unit length.

• Mass of Fluid:

• Weight of Fluid:

Relative Density (Specific Gravity): Ratio of the density of a material to the density of water at 4°C.

• For water at 4°C,

Pressure in Fluids

Pressure is a fundamental concept in fluid mechanics, defined as force per unit area. It is measured in pascals (Pa) in SI units.

• Pressure (P):

• Hydrostatic Pressure: Pressure due to the weight of a fluid column.

• Units: 1 atm = N/m2 = 101.3 kPa; 1 bar = N/m2 = 100.0 kPa

Example: Calculating pressure at depth in the ocean (Titan submersible disaster):

• Given: Depth = 3345 m, Density of seawater ≈ 1.03 g/cm3

• Convert units and use to find Pa = 33 MPa ≈ 333 atm

Young's Modulus and Deformation

Young's modulus quantifies the stiffness of a material under tension or compression.

• Young's Modulus (E):

• Deformation:

• Example: Carbon fiber under pressure (from Titan disaster): mm

Applications: Intravenous Infusions

Fluid pressure is crucial in medical applications such as IV infusions. The height of the IV bag determines the pressure exerted by the fluid.

• Blood pressure in vein: 18 mm Hg = 2394 Pa

• Density of fluid: 1.0 g/mL = 1000 kg/m3

• Required height: m ≈ 1 ft

Measurement of Pressure

Pressure can be measured using various devices, including manometers and gauges. Atmospheric pressure is a reference point for many measurements.

• Gauge Pressure: Pressure relative to atmospheric pressure.

• Atmospheric Pressure: atm

• Example: Tire gauge measures pressure above atmospheric pressure.

Pascal's Principle

Pascal's Principle states that an external pressure applied to a confined fluid is transmitted undiminished throughout the fluid.

• Mechanical Advantage:

• Application: Hydraulic lift for raising cars

Example: Calculating force required on a hydraulic lift:

• Main cylinder diameter: 2.00 cm; Second cylinder diameter: 12.0 cm

• Weight of car: 2000 kg

• Result: N

Pressure Measurement Devices

Common devices for measuring pressure include manometers and tire gauges. These devices compare the pressure of a fluid to atmospheric pressure or use mechanical means (springs) to indicate pressure.

• Manometer: Measures pressure difference using a column of liquid.

• Tire Gauge: Uses a spring to measure the pressure of air in a tire above atmospheric pressure.

• Barometer: Invented by Torricelli; measures atmospheric pressure using a column of mercury (standard: 76.0 cm Hg).

Pressure Unit Conversions

Pressure can be expressed in various units. The following table summarizes key conversion factors.

Additional info: These conversions are essential for solving problems involving pressure in different contexts.