Chapter 3 Fluid Statics
Main Topics Introduction Pressure Variation in a Static Fluid Equilibrium of a fluid of constant density The measurement of Pressure The Barometer Manometers The Bourdon Gauge Other types of Pressure Gauge Uniform Rectilinear Acceleration Pressure Variation in a variable density fluid and the Standard Atmosphere
3.0 Introduction Fluid Statics is a branch of mechanics of fluid which deals primarily with fluids at rest. As individual elements do not move relative to each other, shear stresses are not involved and all forces due to the pressure of the fluid are normal to the surfaces on which they acts.
3.1 Pressure variation in a static fluid Fig.3.1.1 Derivation of (eq.3.1.1) Equation (3.1.1) is the basic equation of fluid statics and it states that the maximum rate of change of pressure occurs in the direction of the gravitational vector.
3.2 Equilibrium of a fluid of constant density Assumptions: Constant density Gravitational acceleration in negative z direction Deriving eq.3.2.1 Assumptions: Constant density (liquid) Gravitational acceleration in negative z direction Relating to liquid surface Deriving eq.3.2.2
3.3 The Measurement of Pressure The Barometer Fig.3.3.1.1 The governing equation is Manometers Fig.3.3.2.1
3.3 The Measurement of Pressure Applying manometer on a pipe Fig.3.3.2.3 The governing equation is The Bourdon Gauge Fig.3.3.3.1 Other types of Pressure Gauge e.g., strain-gage pressure transducer
3.4 Uniform Rectilinear Acceleration Fig.3.1.1* Derivation of eq.3.4.1 Example 3.4.1
3.5 Pressure Variation in a variable-density fluid and the Standard Atmosphere For ideal gas under isothermal condition derivation of (eq.3.5.3) For ideal gas under adiabatic condition governing equations (3.5.4) & (3.5.5) U.S. Standard Atmosphere (Fig.3.5.1) in Troposphere – (eq.3.5.7) in Stratosphere – (eq.3.5.8)
Points to remember The governing equation for static fluid is The above equation applies to static fluid where there is no relative motion between fluid particles. For static fluid, the maximum rate of change of pressure is along the gravitational acceleration and the constant pressure line is perpendicular to the gravitational acceleration. Constant pressure line is for fluid with continuous phase.
Tutorial Link to Tutorial 2