MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

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EXPERIMENT 9 PRESSURE DISTRIBUTION ABOUT A CIRCULAR CYLINDER In many engineering applications, it may be necessary to examine the phenomena occurring when an object is inserted into a flow of fluid. The wings of an airplane in flight, for example, may be analyzed by considering the wings stationary with air moving past them. Certain forces are exerted on the wing by the flowing fluid that tend to lift the wing (called the lift force) and to push the wing in the direction of the flow (drag force). Objects other than wings that are symmetrical with respect to the fluid approach direction, such as a circular cylinder, will experience no lift, only drag. Drag and lift forces are caused by the pressure differences exerted on the stationary object by the flowing fluid. Skin friction between the fluid and the object contributes to the drag force but in many cases can be neglected. The measurement of the pressure distribution existing around a stationary cylinder in an air stream to find the drag force is the object of this experiment. Consider a circular cylinder immersed in a uniform flow. The streamlines about the cylinder are shown in Figure 9.1. The fluid exerts pressure on the front half of the cylinder in an amount that is greater than that exerted on the rear half. The difference in pressure multiplied by the projected frontal area of the cylinder gives the drag force due to pressure (also known as form drag). Because this drag is due primarily to a pressure difference, measurement of the pressure distribution about the cylinder allows for finding the drag force experimentally. A typical pressure distribution is given in Figure 9.2. Shown in Figure 9.2a is the cylinder with lines and arrowheads. The length of the line at any point on the cylinder surface is proportional to the pressure at that point. The direction of the arrowhead indicates that the pressure at the respective point is greater than the free stream pressure (pointing toward the center of the cylinder) or less than the free stream pressure (pointing away). Note the existence of a separation point and a separation region (or wake). The pressure in the back flow region is nearly the same as the pressure at the point of separation. The general result is a net drag force equal to the sum of the forces due to pressure acting on the front half (+) and on the rear half (-) of the cylinder. To find the drag force, it is necessary to sum the components of pressure at each point in the flow direction. Figure 9.2b is a graph of the same data as that in Figure 9.2a except that 9.2b is on a linear grid. Freestream Velocity V Stagnation Streamline Wake FIGURE 9.1. Streamlines of flow about a circular cylinder. separation point p 0 30 60 90 120 150 180 separation point (a) Polar Coordinate Graph (b) Linear Graph FIGURE 9.2. Pressure distribution around a circular cylinder placed in a uniform flow. 24
Pressure Measurement Equipment A Wind Tunnel A Right Circular Cylinder with Pressure Taps Figure 9.3 is a schematic of a wind tunnel. It consists of a nozzle, a test section, a diffuser and a fan. Flow enters the nozzle and passes through flow straighteners and screens. The flow is directed through a test section whose walls are made of a transparent material, usually Plexiglas or glass. An object is placed in the test section for observation. Downstream of the test section is the diffuser followed by the fan. In the tunnel that is used in this experiment, the test section is rectangular and the fan housing is circular. Thus one function of the diffuser is to gradually lead the flow from a rectangular section to a circular one. Figure 9.4 is a schematic of the side view of the circular cylinder. The cylinder is placed in the test section of the wind tunnel which is operated at a preselected velocity. The pressure tap labeled as #1 is placed at 0° directly facing the approach flow. The pressure taps are attached to a manometer board. Only the first 18 taps are connected because the expected profile is symmetric about the 0° line. The manometers will provide readings of pressure at 10° intervals about half the cylinder. For two different approach velocities, measure and record the pressure distribution about the circular cylinder. Plot the pressure distribution on polar coordinate graph paper for both cases. Also graph pressure difference (pressure at the point of interest minus the free stream pressure) as a function of angle θ on linear graph paper. Next, graph ∆p cosθ vs θ (horizontal axis) on linear paper and determine the area under the curve by any convenient method (counting squares or a numerical technique). The drag force can be calculated by integrating the flow-direction-component of each pressure over the area of the cylinder: π D f = 2RL 0 ∫ ∆p cosθdθ The above expression states that the drag force is twice the cylinder radius (2R) times the cylinder length (L) times the area under the curve of ∆p cosθ vs θ. Drag data are usually expressed as drag coefficient C D vs Reynolds number Re. The drag coefficient is defined as D f C D = ρV 2 A/2 The Reynolds number is Re = ρVD µ inlet flow straighteners nozzle test section diffuser fan FIGURE 9.3. A schematic of the wind tunnel used in this experiment. 25
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 and 10: EXPERIMENT 2 FLUID PROPERTIES: VISC
Page 11 and 12: L level R i y zeroing weight torus
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: otameter tank valve motor static pr
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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