If the fluid is considered as a solid object such as a cylinder, the pressure acting on a surface is the same as the pressure on the opposite side of the object, but in a different direction. This condition can be applied to any surface on the imaginary fluid shape. This thus defines that the pressure on a fluid is isotropic, meaning that the force/pressure in any direction applied on the liquid is the same in all directions. Hydrostatic Pressure Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the gravitational pull.
The fluid is known as hydrostatic fluid. The pressure can be calculated from the control volume analysis of a small cube of fluid. It is known that pressure is force applied per unit area P = F/A, and the onlooker acting on any such small cube of fluid is the weight of column above it, we can calculate the hydrostatic pressure by: The summary of the theory is the force on any flat surface is the average pressure acting on the submerged surface multiplied by the area of the submerged surface.
F = Paxar Where: p = water density g = acceleration due to gravity X = vertical distance from free surface to centered of A We know that the magnitude of the distributes force F, which may be considered as a small series of small forces spread over the submerged surface. The sum of the moments of all these small forces about any point must be equivalent to the moment about the same point of the resultant force FRR acting through the point of application, also known as the center of pressure.
Taking the moments about O : Force on strip OAF=XP g AAA Moment of force an strip AM=XP g AAA But we know that : Sum of [xx AAA] = 2nd moment of area (Im) Therefore total moment = page Therefore FRR = page and since FRR = F = p g AX = lama= 2nd moment of area about ‘loll’s moment of area about ’00’ z= from parallel axis theorem elm=lag+ AX Therefore, substituting z- Gig+ AX Gaga+ X Xx=z+q For a partially submerged plate, the same equations apply except that the area of the plate varies. A = BRB) Since Gig = borer And substituting A = BRB and X = or in the equation for z: z= err It can be clearly seen that the centre of pressure is always two-third down the section of the submerged part of the plate. Xx- err+q Procedure: 1- The quadrant is placed on the two dowel pins and the clamping screw is assisted to the balance arm using the clamping screw. L, a, depth d, and width b, of the quadrant end face are measured. 2- With the Perspex tank on the bench, the balance arm is balanced on the knife edges (pivot).
The balance pan is hung from the end of the balance arm. 3- A length of hose is connected from the drain coco to the sump and a length from the bench feed to the triangular aperture on the top of Perspex tank 4- The tank is then leveled using the adjustable feet and spirit level. The counter balance weight is moved until the balance arm is horizontal. – The drain coco is closed and water is admitted until the level reaches the bottom edge of the quadrant. A weight is placed on the balance pan, and water is slowly added into the tank until the balance arm is horizontal.