310105c Pressure 2019 (TF)

Pressure Overview

  • Definition of Pressure: Pressure is defined as force applied per unit area.

  • Formula:

    • Pressure = Force / Area

    • Units:

      • 1 N / 1 m² = Pascal (Pa)

      • 1000 N / 1 m² = 1 kPa (kilopascal)

Calculating Pressure

  • Basic Formula:

    • Pressure = Force / Area

  • Force Calculation:

    • Force (F) can be calculated using Mass (kg) and Gravity (9.81 m/s²):

      • F = Mass x Gravity

Example on Pressure in Fluids

  • Scenario: An actuator with a diaphragm radius of 7” and a force of 4,618 pounds.

  • Pressure Calculation:

    • Pressure = Force / Area = 4,618 lbs / (π × (7 in)²)

    • Result: Convert to other units as needed (30 psi).

Characteristics of Pressure in Fluids

  • Behavior of Fluids:

    • Fluids assume the shape of their container.

    • Gases are compressible under pressure, while liquids are not.

  • Pascal’s Principle: Any external pressure applied to a fluid is transmitted uniformly throughout the fluid.

Vacuum Pressure

  • Definition: Vacuum pressure is the pressure below atmospheric pressure.

  • Formula for Absolute Pressure:

    • Absolute Pressure = Local Absolute Pressure - Vacuum Pressure

    • P_abs = P_atm - P_vac

Gauge Pressure and Fluid Mechanics

  • Gauge Pressure Definition: Difference between absolute pressure and atmospheric pressure.

  • Gauge Pressure Formula:

    • P = P₀ + ρgh

    • Where

      • P = Absolute Pressure

      • P₀ = Atmospheric Pressure

      • ρ = Density of fluid

      • g = Gravitational pull (9.81 N/kg)

      • h = Depth below fluid surface in meters

Example Calculation for Gauge Pressure

  • Calculate pressure at a depth:

    • P = P₀ + ρgh

    • Given: P₀ = 100kPa, h = 100 ft (convert to meters), apply 9.81 m/s² for g

    • Resulting Pressure = 399 kPa at 100 ft depth.

Pressure Conversions

  • Common Conversion Factors:

    • 1 cm = 0.01 m

    • 1 cm² = 10⁻⁴ m²

    • 1 mm = 0.001 m

    • 1 atm = 101.325 kPa = 14.696 psi

Understanding Density

  • Density Formula:

    • ρ = m / V

    • Where:

      • ρ = Density in kg/m³

      • m = Mass in kg

      • V = Volume in m³

  • Relative Density:

    • Relative Density (ρ_r) compares the density of a fluid to that of water.

    • Expressed as ρ_r = ρ / ρ_w where ρ_w is the density of water.

Density Example Calculations

  • Calculating Density:

    • Using the formula ρ = m/V, convert masses and volumes appropriately.

  • Relative Density Calculation:

    • Example: ρ_r = (density of fluid) / (density of water).

Fluid Pressure Formula

  • Fluid Pressure General Formula:

    • P = F/A (where P = pressure, F = force, A = area).

  • Additional pressures include kPa, atm, psi, etc.

Summary of Fluid Pressure and Characteristics

  • Fluid pressure can be affected by depth (h), density (ρ), and gravitational pull (g).

  • Understand the significance of these factors in real-world applications and calculations.