Fluid_Statics & Dynamics.pptx

Lecture Series

1. CEE 205 Fluid Mechanics Fluid Statics

2. Fluid Statics At rest No relative motion Moving with same velocity In statics the particles of fluid is at rest or there is no relative motion between adjacent layers. Hydrostatics Aerostatics

3. Stress Acting in Fluid Statics No Shear stress Only normal stress Significant in gravity fields only

4. Pascal’s Law Pascal's law  states that pressure at any point is the same in all directions and hence it is a scalar quantity in fluid statics. Pascal's law  states that any two points at same elevation in a continuous mass of static fluid will be at the same pressure. Pascal's law  or the principle of transmission of fluid-pressure is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure variations (initial differences) remain the same.

5. Pressure at a Point in Static Fluid

6. Pressure Measurement Reference Absolute Zero or complete Vacuum Absolute Pressure Local Atmospheric Pressure Absolute Pressure Gauge Pressure Negative Gauge Pressure or Vacuum Pressure

7. Pressure Measurement Barometer Manometer

8. Pressure Measurement: Manometer Piezometer U tube manometer Differential manometer Multiple tube manometer Multiple liquid manometer Inclined tube manometer Inverted U tube manometer Manometer with enlarged ends

9. Inclined Tube Manometer

10. Manometer with Enlarged Ends

11. Example: As shown in figure water flows through pipe A and B. The pressure difference of these two points is to be measured by multiple tube manometers. Oil with specific gravity 0.88 is in the upper portion of inverted U-tube and mercury with specific gravity 13.6 in the bottom of both bends. Determine the pressure difference.

12. Pressure Variation in Static Fluid

13. Forces on a Plane Area Immersed in Liquid

14. Total Force and Centre of Pressure

15. Forces on a Curves Surface Immersed in Liquid The horizontal force, FH equals the force on the plane area formed by the projection of the curved surface onto a vertical plane normal to the component. The vertical component equals to the weight of the entire column of fluid, both liquid and atmospheric above the curved surface.

16. Fluid Under Rigid Body Motion In rigid‐body motion, all particles are in combined translation and rotation, and there is no relative motion between particles. The pressure gradient acts in the direction of g – a and lines of constant pressure (including the free surface, if any) are perpendicular to this direction and thus tilted at a downward angle  θ .  

17. Fluid Under Rigid Body Motion

18. Fluid Under Rigid Body Motion

19. Fluid Under Rigid Body Motion: Forced Vortex

20. Fluid Under Rigid Body Motion: Forced Vortex Equations

21. Archimedes Principle: Buoyancy

22. Swimming

23. Stability of Submerged Bodies Unstable Equilibrium Stable Equilibrium Neutral Equilibrium

24. Stability of Floating Bodies Stable Equilibrium GM>0 (M is above G) Unstable Equilibrium GM<0 (M is below G) Neutral Equilibrium GM=0 (M coincides with G)

25. Metacentric Height

26. Euler’s Equation of motion Euler’s equation of motion of an ideal fluid, for a steady flow along a stream line, is basically a relation between velocity, pressure and density of a moving fluid. Euler’s equation of motion is based on the basic concept of Newton’s second law of motion. When fluid will be in motion, there will be following forces associated as mentioned here. 1. Pressure force 2. Gravity force 3. Friction force due to viscosity 4. Force due to turbulence force 5. Force due to compressibility In Euler’s equation of motion, we will consider the forces due to gravity and pressure only. Other forces will be neglected. Assumptions Euler’s equation of motion is based on the following assumptions as mentioned here 1. The fluid is non-viscous. Frictional losses will be zero 2. The fluid is homogeneous and incompressible. 3. Fluid flow is steady, continuous and along the streamline. 4. Fluid flow velocity is uniform over the section 5. Only gravity force and pressure force will be under consideration.

27. Let us consider that fluid is flowing from point A to point B and we have considered here one very small cylindrical section of this fluid flow of length dS and cross-sectional area dA as displayed here in following figure. Let us think about the forces acting on the cylindrical element Pressure force PdA , in the direction of fluid flow Pressure force [P + ( ∂ P/∂S) dS ] dA , in the opposite direction of fluid flow Weight of fluid element (ρ g dA dS )

28. Bernoulli’s Equation from Euler’s: