MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

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EXPERIMENT 3 CENTER OF PRESSURE ON A SUBMERGED PLANE SURFACE Submerged surfaces are found in many engineering applications. Dams, weirs and water gates are familiar examples of submerged surfaces used to control the flow of water. From the design viewpoint, it is important to have a working knowledge of the forces that act on submerged surfaces. A plane surface located beneath the surface of a liquid is subjected to a pressure due to the height of liquid above it, as shown in Figure 3.1. Increasing pressure varies linearly with increasing depth resulting in a pressure distribution that acts on the submerged surface. The analysis of this situation involves determining a force which is equivalent to the pressure, and finding the location of this force. FIGURE 3.1. Pressure distribution on a submerged plane surface and the equivalent force. For this case, it can be shown that the equivalent force is: F = ρgy c A (3.1) in which ρ is the liquid density, y c is the distance from the free surface of the liquid to the centroid of the plane, and A is the area of the plane in contact with liquid. Further, the location of this force y F below the free surface is y F = I xx y c A + y c (3.2) in which I xx is the second area moment of the plane about its centroid. The experimental F y F verification of these equations for force and distance is the subject of this experiment. Center of Pressure Measurement Equipment Center of Pressure Apparatus Weights Figure 3.2 gives a schematic of the apparatus used in this experiment. The torus and balance arm are placed on top of the tank. Note that the pivot point for the balance arm is the point of contact between the rod and the top of the tank. The zeroing weight is adjusted to level the balance arm. Water is then added to a predetermined depth. Weights are placed on the weight hanger to re-level the balance arm. The amount of needed weight and depth of water are then recorded. The procedure is then repeated for four other depths. (Remember to record the distance from the pivot point to the free surface for each case.) From the depth measurement, the equivalent force and its location are calculated using Equations 3.1 and 3.2. Summing moments about the pivot allows for a comparison between the theoretical and actual force exerted. Referring to Figure 3.2, we have WL F = (y + y F ) (3.3) where y is the distance from the pivot point to the free surface, y F is the distance from the free surface to the line of action of the force F, and L is the distance from the pivot point to the line of action of the weight W. Note that both curved surfaces of the torus are circular with centers at the pivot point. For the report, compare the force obtained with Equation 3.1 to that obtained with Equation 3.3. When using Equation 3.3, it will be necessary to use Equation 3.2 for y F . Questions 1. In summing moments, why isn't the buoyant force taken into account? 2. Why isn’t the weight of the torus and the balance arm taken into account? 10
L level R i y zeroing weight torus pivot point (point of contact) weight hanger R o y F h F w FIGURE 3.2. A schematic of the center of pressure apparatus. 11
Page 1 and 2: A Manual for the MECHANICS of FLUID
Page 3 and 4: TABLE OF CONTENTS Item Page Report
Page 5 and 6: as its strong points. Suggest exten
Page 7 and 8: EXPERIMENT 1 FLUID PROPERTIES: DENS
Page 9: EXPERIMENT 2 FLUID PROPERTIES: VISC
Page 13 and 14: 5. Is a low value of the standard d
Page 15 and 16: pivot balancing weight lever arm wi
Page 17 and 18: Questions 1. Can a similar procedur
Page 19 and 20: actual flow rate (measured in the l
Page 21 and 22: manometer orifice meter venturi met
Page 23 and 24: otameter tank valve motor static pr
Page 25 and 26: Pressure Measurement Equipment A Wi
Page 27 and 28: EXPERIMENT 10 DRAG FORCE DETERMINAT
Page 29 and 30: Experiment II For a number of wings
Page 31 and 32: axis) versus (Q 2 /b 2 h 0 3 g). De
Page 33 and 34: Therefore, Q = ∫ 0 Integration gi
Page 35 and 36: Develop a hydraulic jump in the cha
Page 37 and 38: At any upstream (of the hump) locat
Page 39 and 40: EXPERIMENT 16 MEASUREMENT OF VELOCI
Page 41 and 42: Incompressible Flow Through a Meter
Page 43 and 44: TABLE 16.1. Summary of equations fo
Page 45 and 46: placed on the torque arm to reposit
Page 47 and 48: ∆H = H 2 - H 1 = p 2 ρg + V 2 2
Page 49 and 50: Specific Speed A dimensionless grou
Page 51 and 52: 1 large orifice volume flow rate in

MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

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