Fluid Mechanics Quiz

Fluid Mechanics

• Fluid mechanics is the study of fluids (liquids and gases) and their behavior.

Density

• Density (ρ) is a measure of compactness of matter.
• ρ = m/V (definition of density)
• Specific Gravity is a measure of the density of a substance compared to the density of water.
  • If a liquid has a specific gravity of 1.2, it means it is 1.2 times as dense as water.
  • Two objects made of the same material have the same density even though they may have different masses and different volumes.

Densities of Common Substances

(Table of densities in kg/m³ for various substances)

• Air: 1.20
• Ethanol: 0.81 × 10³
• Benzene: 0.90 × 10³
• Ice: 0.92 × 10³
• Water: 1.00 × 10³
• Seawater: 1.03 × 10³
• Blood: 1.06 × 10³
• Iron/Steel: 7.8 × 10³
• Brass: 8.6 × 10³
• Copper: 8.9 × 10³
• Silver: 10.5 × 10³
• Lead: 11.3 × 10³
• Mercury: 13.6 × 10³
• Gold: 19.3 × 10³

Pressure in a Fluid

• Pressure in a fluid is a measure of force distribution over an area.
• 1 pascal (Pa) = 1 N/m²
• 1 atm = 1.013 × 10⁵ Pa
• 1.013 bar = 1013 millibar = 14.70 lb/in.²
• Atmospheric pressure is the pressure of Earth's atmosphere and varies with weather and elevation.

Pressure, Depth, and Pascal's Law

• p = p₀ + ρgh (pressure in a fluid of uniform density)
  • p₀ is the pressure at the surface.
  • ρ is the density.
  • g is the acceleration due to gravity.
  • h is the depth.
• "The pressure p at the depth h is greater than the pressure p₀ by an amount ρgh."
• Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and walls of the containing vessels.

Gauge, Absolute, and Atmospheric Pressure

• Gauge pressure is the pressure of a system above atmospheric pressure (Pabsolute – Patmospheric).
• Absolute pressure is the total pressure exerted on a system (Pgauge + Patmospheric).

Example - Manometer

• A manometer measures pressure differences.
• In a manometer with water and oil, the relationship between the heights of the liquids is: hoil = (Pwater / P oil) × hwater

Buoyancy and Archimedes's Principle

• Buoyancy is the apparent loss of weight due to an upward force exerted by the fluid, called the Buoyant Force.
• Archimedes's principle states that when a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

Fluid Flow

• Ideal fluid is incompressible (density cannot change) and no internal friction.
• Laminar and Turbulent flow are types of fluid flows.
• The continuity equation (A₁v₁ = A₂v₂) describes the relationship between flow speed and cross-sectional area in an incompressible fluid.

Bernoulli's Equation

• Bernoulli's equation relates pressure, flow speed, and height for the flow of an ideal, incompressible fluid.
• It's useful in plumbing systems, hydroelectric stations, and airplane flight.
  • P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂²
  • where P is pressure, ρ is density, g is acceleration due to gravity, y is height, and v is velocity
  • Static, Dynamic and Hydrostatic pressures are components of Bernoulli's equation.