Basic fluids mechanics

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• Engineering Fluid Mechanics
• © 2012 T. Al-Shemmeri & Ventus Publishing ApS
• ISBN 978-87-403-0114-4
• Contents


  • Notation
  • Fluid Statics
  • Internal Fluid Flow
  • External Fluid Flow
  • Compressible Fluid Dynamics
  • Hydroelectric Power
  • Sample Examination paper
  • Formulae Sheet
• Notation


  Definitions of symbols used in the book
• Any physical situation can be described in terms of measurable properties known as variables
• Variables can be basic like length and time, or derived like velocity
• Basic SI Units


  • Mass
  • Length
  • Time
  • Electric current
  • Temperature
  • Luminous intensity
• Derived SI Units with Special Names


  • Force
  • Work, energy
  • Power
  • Pressure
• Other Derived SI Units

  • Area
  • Volume
  • Density
  • Angular acceleration
  • Velocity
  • Pressure, stress
  • Kinematic viscosity
  • Dynamic viscosity
  • Momentum
  • Kinetic energy
  • Specific enthalpy
  • Specific entropy
• Non-SI Units


  • Time
  • Temperature
  • Angle
  • Volume
  • Speed
  • Angular speed
  • Frequency
  • Pressure
  • Kinematic viscosity
  • Dynamic viscosity
• Prefixes for Multiples of Units

  • exa
  • Peta
  • tera
  • giga
  • mega
  • kilo
  • hecto
  • deca
  • deci
  • centi
  • milli
  • micro
  • nano
  • pico
  • fempto
  • atto
• Conversion Factors


  • Length
  • Mass
  • Area
  • Volume
  • Force, Weight
  • Density
  • Velocity
  • Pressure, Stress
  • Power
  • Moment, Torque
  • Rates of Flow
  • Fuel Consumption
  • Kinematic Viscosity
  • Dynamic Viscosity
  • Energy
• Conversion Factors


  Allows converting between different units of measurement
• Units


  • Length (L)
  • Area (A)
  • Volume (V)
  • Mass (M)
  • Force (F)
  • Velocity (V)
  • Volume Flow
  • Pressure (P)
  • Density (ρ)
  • Heat Flow Rate
  • Thermal Conductivity (k)
  • Thermal Conductance (U)
  • Enthalpy (h)
• Converting between units


  1. Multiply by X Factor

  2. = Unit
• Force (F)


  • lb. to N
• Velocity (V)


  • ft/min to m/sec
• Volume Flow


  • Imp gal/min to litres/s
  • Imp gal/h to m3/s
  • ft3/min to m3/s
• Density (ρ)


  • lb/ft3 to kg/m3
• Heat Flow Rate


  • Btu/h to W
  • kcal/h to W
• Thermal Conductivity (k)


  • Btu/ft h R to W/m K
  • kcal/m h K to W/m K
• Thermal Conductance (U)


  • Btu/h ft2 R to W/m2 K
  • kcal/h m2 K to W/m2 K
• Simply multiply the imperial by a constant factor to convert into Metric or the other way around
• Compressible fluid


  Fluid which changes its volume appreciably under the application of pressure
• Bulk modulus of elasticity (E)

  Ratio of the change in unit pressure to the corresponding volume change per unit volume
• Pascal's law


  The pressure intensity at a point in a fluid at rest is the same in all directions
• Pascal's law proof


  1. Resolve forces vertically

  2. Resolve forces horizontally
• Fluid-static law


  The pressure in a fluid increases with increasing depth
• Calculating pressure in a fluid column

  1. Force on base = Weight of Column of Fluid

  2. Weight of column = mass x acceleration due to gravity

  3. Mass of fluid column = density x volume

  4. Volume of column = Area x height

  5. Pressure = density x gravity x height
• Pressure transducer


  Device that, being activated by energy from the fluid system, responds in a manner related to the magnitude of the applied pressure
• Bourdon gauge


  Mechanical pressure measurement device that relies on a circular arc of elliptical cross-section tube changing shape under fluid pressure
• Manometer


  Device that indicates pressure by the displacement of a manometric fluid
• Calculating pressure using manometers

  1. U-tube: P1 - P2 = ρgh

  2. Well-type: P1 - P2 = ρgh(1 + d/D)

  3. Inclined tube: P1 - P2 = ρgL sin(θ)
• Hydraulic brakes


  • Pressure applied on brake pedal is transmitted undiminished to brake pads
  • Sliding friction between tyres and road opposes forward motion
• Hydraulic lift


  • Force applied on small cylinder creates pressure that acts upwards on large cylinder, producing a much larger upward force
• Centre of pressure


  Point at which the total force on a submerged surface acts
• Calculating centre of pressure

  1. Take moments about a point

  2. Use 2nd moment of area formula

  3. Relate to centre of gravity
• Centre of pressure is always below the centre of gravity