Introduction to Fluid Mechanics Chapter 3 Fluid Statics

Introduction to Fluid Mechanics Chapter 3 Fluid Statics © John Wiley and Sons, Inc.

Main Topics ü The Basic Equations of Fluid Statics ü Pressure Variation in a Static Fluid ü Hydrostatic Force on Submerged Surfaces ü Buoyancy © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Body Force The aim is to derive an equation for computing the pressure field in a static fluid. Two general types of forces may be applied to a fluid, body force and surface forces. © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Surface Force In a static fluid there are no shear stresses, so the only surface force is the pressure force. © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Surface Force © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Surface Force © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Total Force © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Newton’s Second Law © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics ü Pressure-Height Relation Restrictions: 1. Static fluid. 2. Gravity is the only body force. 3. The z axis is vertical and upward. © John Wiley and Sons, Inc.

The Basic Equations of Fluid Statics Pressure values must be stated with respect to a reference level. If the reference level is a vacuum, pressures are termed absolute, as shown in Fig. 3. 2. Most pressure gages indicate a pressure difference - the difference between the measured pressure and the ambient level (usually atmospheric pressure). © John Wiley and Sons, Inc.

The Standard Atmosphere Scientists and engineers sometimes need a numerical or analytical model of the Earth’ s atmosphere. © John Wiley and Sons, Inc.

Pressure Variation in a Static Fluid ü Incompressible Fluid: Manometers © John Wiley and Sons, Inc.

Pressure Variation in a Static Fluid ü Compressible Fluid: Ideal Gas Need additional information, e. g. , T(z) for atmosphere © John Wiley and Sons, Inc.

Pressure Variation in a Static Fluid In the U. S. Standard Atmosphere the temperature decreases linearly with altitude up to an elevation of 11. 0 km. For a linear temperature variation with altitude given by T =T 0−mz , we obtain: © John Wiley and Sons, Inc.

Hydrostatic Force on Submerged Surfaces ü Plane Submerged Surface We can examine the force on a surface submerged in a liquid. © John Wiley and Sons, Inc.

Hydrostatic Force on Submerged Surfaces ü Plane Submerged Surface © John Wiley and Sons, Inc.

Hydrostatic Force on Submerged Surfaces ü Plane Submerged Surface • Algebraic Equations – Total Pressure Force Where pc is the absolute pressure in the liquid at the location of the centroid of area. © John Wiley and Sons, Inc.

Hydrostatic Force on Submerged Surfaces ü Plane Submerged Surface • Algebraic Equations – Net Pressure Force © John Wiley and Sons, Inc.

Hydrostatic Force on Submerged Surfaces ü Curved Submerged Surface The pressure force is normal to the surface at each point, but now the infinitesimal area elements point in varying directions. © John Wiley and Sons, Inc.

Hydrostatic Force on Submerged Surfaces ü Curved Submerged Surface • Horizontal Force = Equivalent Vertical Plane Force • Vertical Force = Weight of Fluid Directly Above (+ Free Surface Pressure Force) © John Wiley and Sons, Inc.

Buoyancy If an object is immersed in a liquid, or floating on its surface, the net vertical force acting on it due to liquid pressure is termed buoyancy. © John Wiley and Sons, Inc.

Buoyancy For a submerged body the buoyancy force of the fluid is equal to the weight of displaced fluid. Example 3. 8 demonstrates the buoyancy of a hot air baloon © John Wiley and Sons, Inc.