Machine

• Pressure


  The normal component of force per unit area
• Pressure in a fluid at rest is the same in all directions
• Defining pressure


  Limit of the ratio of the normal component of force to the area as the area approaches zero
• Pascal (Pa)


  Unit of pressure in the International System, equal to 1 N/m²
• Bar


  Unit of pressure, equal to 10⁵ Pa or 0.1 MPa
• Standard atmosphere (atm)


  Unit of pressure, equal to 101,325 Pa or 14.696 lb/in²
• Pressure in a gas-filled cylinder with a movable piston


  1. Pressure is fixed by the external force acting on the piston

  2. Product of pressure and piston area must equal the external force

  3. If external force changes, gas pressure and piston position adjust to establish a new force balance
• Gas in the cylinder is heated by an outside body


  Pressure increases, causing the piston to move
• Hydraulic piston/cylinder system


  • Cylinder diameter of 0.1 m
  • Piston and rod mass of 25 kg
  • Rod diameter of 0.01 m
  • Outside atmospheric pressure of 101 kPa
  • Inside hydraulic fluid pressure of 250 kPa
• Calculating the force the rod can push with in the upward direction


  1. Assume static balance of forces on the piston (positive upward)

  2. Fatma=0

  3. Pot At-PA-A)-F-mg

  4. Po (Ag-Are)

  5. Solve for F
• Areas


  • Ag = π D²/4 = 0.007 854 m²
  • Ar = π d²/4 = 0.000 078 54 m²
• The force becomes F = 1963.5 - 785.32 - 245.25 = -932.9 N
• Muscle contraction is the shortening of a muscle fibre, which occurs when actin filaments slide past myosin filaments
• Skeletal muscles are attached to bones by tendons
• Absolute pressure


  The pressure of a system, used in thermodynamic relations
• Gage pressure


  The difference between the absolute pressure of a system and the absolute pressure of the atmosphere existing outside the measuring device
• When the pressure of the system is greater than the local atmospheric pressure


  The term gage pressure is used
• Vacuum pressure


  The difference between the absolute pressure of the atmosphere and the absolute pressure of the system, when the local atmospheric pressure is greater than the pressure of the system
• Engineers in the United States frequently use the letters a and g to distinguish between absolute and gage pressures
• Absolute and gage pressures in pounds force per square inch


  • psia
  • psig
• Calculating the force acting downward at the bottom of a column of fluid

  1. PA + mg

  2. PA + ρAgH
• m


  Mass of the fluid column
• A


  Cross-sectional area of the fluid column
• ρ


  Density of the fluid column
• The force on the fluid column

  Must be balanced by the upward force at the bottom of the column, which is PA
• Since points A and B are at the same elevation in a column of the same fluid, their pressure must be equal (the fluid being measured in the vessel has a much lower density, such that its pressure P is equal to P₁)
• For distinguishing between absolute and gauge pressure in this book, the term pascal will always refer to absolute pressure. Any gauge pressure will be indicated as such.
• Barometer


  Used to measure atmospheric pressure
• ρ


  Density of mercury at 25°C = 13,534 kg/m³
• g = 9.807 m/s²
• Mercury (Hg) manometer


  Used to measure the pressure in a vessel
• Mercury manometer


  • Mercury has a density of 13 590 kg/m³
  • Height difference between the two columns is measured to be 24 cm
• Determining the pressure inside the vessel


  1. Measure the gauge pressure as a pressure difference

  2. Calculate the gauge pressure using Eq. 1.2: pgH

  3. Convert the gauge pressure to absolute pressure by adding the atmospheric pressure
• Gauge pressure = 31 985 Pa = 31.985 kPa
• Atmospheric pressure measured by a barometer is 750 mm Hg
• Absolute pressure in the vessel = 131 940 Pa = 1.302 atm
• Pressure


  The force per unit area exerted on a surface
• Pressure at the bottom of a 7.5-m-tall storage tank


  • For gasoline with atmospheric pressure 101 kPa on the top surface
  • For liquid refrigerant R-134a with 1 MPa pressure on the top surface
• Fluid


  • Gasoline with density 750 kg/m³
  • Liquid refrigerant R-134a with density 1206 kg/m³
• Calculating pressure difference due to gravity


  Use Eq. 1.2: ΔP = ρgh