Chapter 10: Fluids

10-1 Phases of Matter

The three common phases of matter are solid, liquid, and gas. Each phase has distinct physical properties that affect its behavior in various environments.

• Solid: Has a definite shape and size due to strong intermolecular forces.

• Liquid: Has a fixed volume but can take the shape of its container.

• Gas: Can be compressed easily and takes both the shape and volume of its container.

• Fluids: Liquids and gases are both classified as fluids because they can flow.

10-2 Density and Specific Gravity

Density is a measure of how much mass is contained in a given volume. Specific gravity compares the density of a substance to that of water.

• Density formula:

• SI unit: kg/m3; also commonly expressed in g/cm3 (1 g/cm3 = 1000 kg/m3).

• Water at 4°C: Density is 1 g/cm3 = 1000 kg/m3.

• Specific gravity:

10-3 Pressure in Fluids

Pressure in fluids is the force exerted per unit area. It is a scalar quantity and is uniform in all directions at a given depth in a fluid at rest.

• Pressure formula:

• SI unit: Pascal (Pa), where

• Pressure is the same in every direction at a given depth; otherwise, the fluid would flow.

• For a fluid at rest, there is no force component parallel to any solid surface.

• Pressure at depth: (valid for liquids of constant density)

Example: If the surface of water in a tank is 30 m above a faucet, the pressure difference is .

10-4 Atmospheric Pressure and Gauge Pressure

Atmospheric pressure is the pressure exerted by the weight of the atmosphere. Gauge pressure is the pressure measured above atmospheric pressure.

• At sea level, atmospheric pressure is about (1 atm).

• Another unit:

• Standard atmospheric pressure is just over 1 bar.

• Cells maintain internal pressure to balance atmospheric pressure.

• Absolute pressure: (atmospheric + gauge pressure)

10-5 Pascal’s Principle

Pascal’s Principle states that if an external pressure is applied to a confined fluid, the pressure increases equally at every point in the fluid. This principle is fundamental in hydraulic systems.

• Used in hydraulic lifts and hydraulic brakes.

• Allows multiplication of force in hydraulic machines.

10-6 Measurement of Pressure; Gauges and the Barometer

Pressure can be measured using various devices, each suited for different applications.

• Open-tube manometer: Measures pressure relative to atmospheric pressure by the height difference of a liquid column.

• Aneroid gauge: Uses a flexible chamber to measure air pressure; often used as a barometer.

• Tire gauge: Measures the pressure of air in tires using a spring mechanism.

• Mercury barometer: Developed by Torricelli; measures atmospheric pressure by the height of a mercury column (1 atm ≈ 76 cm Hg).

• Any liquid can be used in a barometer, but denser liquids are more convenient.

10-7 Buoyancy and Archimedes’ Principle

Buoyancy is the upward force exerted by a fluid on a submerged object. Archimedes’ Principle states that the buoyant force equals the weight of the fluid displaced by the object.

• Buoyant force formula:

• Net force on the object:

• If the object's density is less than the fluid, it will float; otherwise, it will sink.

• For floating objects, the fraction submerged is .

• This principle applies to gases as well, explaining why hot-air and helium balloons rise.

Example: Two balls of equal radius (aluminum and steel) at the bottom of a lake experience the same buoyancy force, as buoyancy depends only on the volume displaced, not the material.

10-8 Fluids in Motion; Flow Rate and the Equation of Continuity

Fluid motion can be laminar (smooth) or turbulent (chaotic with eddies). The flow rate is the mass of fluid passing a point per unit time, and the equation of continuity ensures conservation of mass in fluid flow.

• Laminar flow: Smooth, orderly movement of fluid.

• Turbulent flow: Irregular, with eddies; higher viscosity.

• Equation of continuity:

• If density is constant:

• Where the pipe is wider, the fluid flows slower.

10-9 Bernoulli’s Equation

Bernoulli’s Equation relates the pressure, velocity, and height of a fluid in steady flow, expressing conservation of energy for fluids.

• Bernoulli’s equation:

• As fluid speed increases, pressure decreases.

10-10 Applications of Bernoulli’s Principle: Torricelli, Airplanes, Baseballs, Blood Flow

Bernoulli’s principle has many practical applications, including fluid speed from tanks, lift on airplane wings, and blood flow in arteries.

• Torricelli’s theorem: The speed of fluid exiting a hole in a tank is

• Lift on airplane wings: Caused by different air speeds and pressures above and below the wing, resulting in upward force.

Additional info:

• Questions and figures included in the file reinforce concepts such as pressure, buoyancy, and fluid equilibrium.

• Tables and diagrams (e.g., manometers, barometers, U-tubes) are used to illustrate measurement and comparison of fluid properties.