Recap: Fluid Statics | Fluid Mechanics for Mechanical Engineering PDF Download

Recap
  In this course you have learnt the following 

• Forces acting on a fluid element in isolation are of two types;   
             •  Body force : Body forces act over the entire volume of the fluid element and are caused by external agencies
            •   Surface force. Surface forces, resulting from the action of surrounding mass on the fluid element, appear on its surfaces
• Normal stresses at any point in a fluid at rest, being directed towards the point from all directions, are of equal magnitude. The scalar magnitude of the stress is known as hydrostatic or thermodynamic pressure.
• The fundamental equations of fluid statics are written as   
•  with respect to a cartesian frame of reference with x - y plane as horizontal and axis z being directed vertically upwards. For an incompressible fluid, pressure P at a depth h below the free surface can be written as p = Po + ρ gh, where Po is the local atmospheric pressure.
   
• At sea-level, the international standard atmospheric pressure has been chosen as Patm = 101.32 kN/m2. The pressure expressed as the difference between its value and the local atmospheric pressure is known as gauge pressure.
   
• Piezometer tube measures the gauge pressure of a flowing liquid in terms of the height of liquid column. Manometers are devices in which columns of a suitable liquid are used to measure the difference in pressure between two points or between a certain point and the atmosphere. A simple U-tube manometer is modified as inclined tube manometer, inverted tube manometer and micro manometer to measure a small difference in pressure through a relatively large deflection of liquid columns.
   
• The hydrostatic force on anyone side of a submerged plane surface is equal to the product of the area and the pressure at the centre of area. The force acts in a direction perpendicular to the surface and its point of action, known as pressure centre, is always at a higher depth than that at which the centre of area lies. The distance of centre of pressure from the centre of area along the axis of symmetry is given by 
  
   
• For a curved surface, the component of hydrostatic force in any horizontal direction is equal to the hydrostatic force on the projected plane surface on a vertical plane perpendicular to that direction and acts through the centre of pressure for the projected plane area. The vertical component of hydrostatic force on a submerged curved surface is equal to the weight of the liquid volume vertically above the submerged surface to the level of the free surface of liquid and acts through the centre of gravity of the liquid in that volume.
   
• When a solid body is either wholly or partially immersed in a fluid, the hydrostatic lift due to net vertical component of the hydrostatic pressure forces experienced by the body is called the buoyant force. The buoyant force on a submerged or floating body is equal to the weight of liquid displaced by the body and acts vertically upward through the centroid of displaced volume known as centre of buoyancy.
   

• The equilibrium of floating or submerged bodies requires that the weight of the body acting through its centre of gravity has to be colinear with an equal buoyant force acting through the centre of buoyancy. A submerged body will be in stable, unstable or neutral equilibrium if its centre of gravity is below, above or coincident with the centre of buoyancy respectively. Metacentre of a floating body is defined as the point of intersection of the centre line of cross-section containing the centre of gravity and centre of buoyancy with the vertical line through new centre of buoyancy due to any small angular displacement of the body. For stable equilibrium of floating bodies, metacentre M has to be above the centre of gravity G. M coinciding with G or lying below G refers to the situation of neutral and unstable equilibrium respectively. The distance of metacentre from centre of gravity along the centre line of cross-section is known as metacentric height and is given by.