Hydrostatic force - Centre of Pressure Lab Report

Hydrostatic Forces – Centre of Pressure Introduction Many engineering structures such as dams, flood control gates and fluid storage tanks are essential components of large hydraulic structures. Many of these structures are constructed to provide water supply and irrigation and they play an important role in maintaining the well-being of mankind. The design of these components necessitates the understanding of how fluid forces act. Such designs require not only determination of the magnitude of the resultant force but also its point of action, which is known as the “centre of pressure” (y P). With this information, engineers can design the hydraulic structure to withstand the hydrostatic forces. In this experiment, you will be using an immersed quadrant tank (Figure 1) pivoted at a knife-edge pivot to determine the centre of pressure for different values of hydrostatic force. This is achieved by computing the moment, M required to counter the moment induced by the hydrostatic force due to water acting on the quadrant tank. The restoring (counter-clockwise) moment needed to overcome the clockwise moment (about the pivot) caused by water is effected by placing known weights on the left-hand end of the apparatus. In the experiment, if the clockwise moment (induced by water) just balances the counter-clockwise moment (caused by the weights), the moment arm and hence the centre of pressure can be computed. The latter can then be compared with that calculated theoretically.

Figure 1. Hydrostatic Forces Apparatus – Quadrant Tank Objective 

To determine the hydrostatic thrust acting on a plane surface immersed in water



To determine the position of the line of action of the thrust (centre of pressure) and to compare the position determined experimentally and that determined theoretically.

Theory The diagrammatic representation of the apparatus is shown in Figure 2 below.

Figure 2. Dimensions of Quadrant Tank Considering the physics governing the hydrostatic forces acting on the quadrant tank, and the moments exerted about the pivot, it is important to recognize that there are two different cases: 1. Partly submerged 2. Fully submerged Whilst the theory governing both these cases is the same, it is however clearer to consider them separately. Before we go into the detail of considering the forces and moments, it is important to reiterate that the moments exerted by water on the curve surfaces of the quadrant tank about the pivot point is zero. This is because the hydrostatic force acting on any point on the quadrant is normal to the tangent to that point. Hence the resultant force acting on the curve portion of the quadrant tank has no moment arm about the pivot axis (the pivot is located at the centre of the quarter-circle). Therefore, the only moment exerted by water about the pivot point is caused by the horizontal thrust acting on the vertical face of the quadrant tank. In conducting the computation, we need to do equate the moment caused by the horizontal thrust about the pivot point to that induced by the weight on the balance pan. First case: Partly Submerged Vertical Plane Surface

Figure 3 shows the diagrammatic representation of the apparatus when the quadrant tank is partially submerged. This refers to the condition where the water level is equal to or less than the top level of the vertical face of the quadrant tank.

Figure 3. Partly Submerged Vertical Plane Surface Symbols in Figure 3 are defines as below: d = depth of the immersion (for partially submerged case, d