[O04-P15] Comparison of Fluid Resistance and Experience for Calculation of Resistance Coefficient according to Object Shape
Keywords:Fluid dynamics, Air resistance, Resistance coefficient, Cone
Next, we focused on the cones in the above six kinds of shapes. Cones are one of the most useful shapes in daily life. We can easily reproduce several patterns of apex angles. Therefore, we attempted to estimate the values of the fluid resistance coefficient in conjunction with the apex angles using two methods. One method is hitting the object with fluid and the other is calculating the coefficient from the terminal velocity of the falling object. We called these Experiment 3 and 4, respectively.
In Experiment 3, eight types of objects (Table 2) with different central angles were made with the 3D printer. The cones were suspended by spring scales, and we poured water fallen freely on them from a position a certain distance away from the objects. When water is allowed to fall freely on the top of an object, the pressure applied to the object is measured in gram weight units, and the pressure can be calculated. The resistance coefficient was calculated from the experimental results, and a graph corresponding to the change in the central angle was created (Fig 1). Fig 1 shows a curve in which the resistance coefficient increases exponentially with the increase in the central angle. Also, the resistance coefficient obtained in the experiment was displayed using function display software (FunctionView Ver 6.02), and the approximate function was predicted to obtain the equation to calculate resistance coefficient. Exponential function expressions are cumbersome and the accuracy of the approximate expression is not known. To simplify the calculation and use the standard deviation to estimate the expression more accurately, a first-order approximation using logarithms is used. An approximation using logarithms to make calculations is easier and to use the standard deviation estimates a more accurate expression. Further, the value of the resistance coefficient obtained in Experiment 3 was lower than the value described in the above reference book or the like. As the reason, we thought to be that the area that the dropped water hits is smaller than the projected area of the object, and that there is a diffrence in the force between "the object moving in the fluid" and "the fluid hitting the stopped object".
In Experiment 4, we prepared cones with no bottoms (hollow cones) with different apex angles made of copy paper (PPC paper) of uniform thickness. And we experimented in the same place in the author's house for the whole experiment (no wind, indoors). After dropping the object from a height of 2.5 meters above the floor, the speed reached terminal velocity at 2.0 meters above the floor. We measured the time taken from 2.0 meters above the floor to the landing. The terminal velocity is calculated from the measured time, and the resistance coefficient is obtained. In Experiment 4, as in Experiment 3, we will create a graph which shows relationship between central angle and resistance coefficient, and predict approximated equation using the function software.