HYDROSTATIC LAW OF FORCE OF A FLUID PARTICLES

HYDROSTATIC LAW OF FORCE

1. Lecture 6 Hydrostatic forces on surfaces – total pressure and centre of pressure. Horizontal- vertical and inclined plane surface

2. When a static mass of fluid comes in contact with a surface, either plane or curved, a force is exerted by the fluid on the surface known as total pressure . For a fluid at rest no tangential force exists , the total pressure acts in the direction normal to the surface. The point of application of total pressure on the surface is known as centre of pressure .

3. Consider on the plane surface a horizontal strip of thickness dx and width b lying at a vertical depth x below the free surface of the liquid. Since the thickness of the strip is very small, for this strip the pressure intensity may be assumed to be constant equal to p = w. x. The area of the strip being dA = (b.dx) The total pressure on the strip = p. dA = w .x. (b. dx)

4. .'. Total pressure on the entire plane surface is P = The total pressure on a vertical plane surface is equal to the product of the area of the surface and the intensity of pressure at the centroid of the area. Total pressure on a horizontal plane surface

5. The point of application of the total pressure on a plane surface is known as centre of pressure. For a plane surface immersed vertically the centre of pressure does not coincide with the centroid of the area. Since the pressure intensity increases with the increase in depth of liquid , the centre of pressure for a vertically immersed plane surface lies below the centroid of the surface area.

6. When a static mass of fluid comes in contact with a surface, either plane or curved , a force is exerted by the fluid on the surface. This force is known as total pressure. The point of application of total pressure on the surface is known as Centre of pressure. Total pressure is the numerical sum of all the forces acting on all the sides of the surface. The sum of the forces acting on a surface considering the directions, will give us the resultant force or the resultant pressure on the given surface.

7. Lecture 7 Pressure diagram – total pressure on curved surface

8. Total pressure on curved surface Consider a curved surface wholly submerged in a static mass of liquid of specific weight w and dA is the area of a small element of the curved surface lying at a vertical depth h below the free surface of liquid. Total pressure on elementary area dp = pdA = wh dA acting normal to the surface  

9. Resolve total pressure p on horizontal surface into the horizontal and vertical components P H & P v . dp can also be resolved into horizontal & vertical components dP H = dp sin  = pdA sin  dpv = dp cos  = pda cos   is the inclination of the elementary area with horizontal p = wh P H = Pv = Pv =

10. (dA sin  ) is the vertical projection of the elementary area dA (dA cos ) is the horizontal projection of the elementary are dA (wh) dA sin  is the total pressure. On the vertical projection of the element area dA dA sin  is the total pressure. On the projected area of curved surface on vertical plane P H = total pressure. on the projected area of the curved surface on vertical plane (CD) (wh) dA cos  - total pressure. on horizontal projection of elementary area dA ʃdA sin  - total pressure. on weight of liquid lying above the curved surface in the portion ABCDEFA. And direction of the resultant force p is Q = tan -1  is the angle made by the resultant force p with the horizontal