Aquino, Ivan I. BSME 3-1 1. Derived the below equation. Use water as the liquid. 2. Compute the pressure in psi at the bottom of each column and explain why they have different results. Aquino, Ivan I. BSME 3-1 Since their specific gravities differ, they have the same static head but varying pressure. As illustrated in Figure 1, we have several liquid varieties. salt water, water, and gasoline are a few examples. As a result, these liquids' specific gravity is determined by their density. Despite having the same static head in feet, each distinct liquid has a different pressure because of its unique specific gravity. 1. What is similitude? (15 pts) Similitude is essentially the degree to which a model resembles its prototype in every way. It implies to us that the properties of the model and the prototype will be similar, or we may argue that similitude explains that the model and prototype would be same in every way. 2. What is the difference between model and the prototype? (15 pts) • Prototype is the physical structure for which engineering design is required. The predictions are made for the prototype to work under actual field conditions. • Model is the scale down representation of any physical structure. A model is smaller than the prototype so as to conduct laboratory studies and it is less expensive to construct and operate. Sometimes size of model can be larger than the prototype if amplified and more focused studies have to be carried out. 3. What are the three types of similarities? Explain each briefly. (50 pts) Three types of similarities must exist between model and prototype. These are the: a. Geometric similarity – it is the similarity of shape. Geometric similarity is said to exist between model and prototype, if the ratio of all respective linear dimension in model and prototype are equal. - A model and prototype are geometric similar if and only if all body dimensions in all three coordinates have the same linear-scale ratio. It requires that the model and the prototype be of the same shape and that all the linear dimensions of the model be related to corresponding dimensions of the prototype by a constant scale factor. Usually, one or more of these pi terms will involve ratios of important lengths, which are purely geometrical in nature. b. Kinematic Similarity – it is said to exist between model and prototype, if the ratios of velocity and acceleration at a point in model and at the respective point in the prototype are the same. - The motions of two systems are kinematically similar if homogeneous particles lie at homogeneous points at homogeneous times. In a specific sense, the velocities at corresponding points are in the same direction and are related in magnitude by a constant scale factor. This also requires that streamline patterns must be related by a constant scale factor. The flows that are kinematically Aquino, Ivan I. BSME 3-1 similar must be geometric similar because boundaries form the bounding streamlines. The factors like compressibility or cavitation must be taken care of to maintain the kinematic similarity. c. Dynamic Similarity – it is said to exist between model and prototype, if the ratios of corresponding forces acting at the corresponding points are the same. - When two flows have force distributions such that identical types of forces are parallel and are related in magnitude by a constant scale factor at all corresponding points, then the flows are dynamic similar. For a model and prototype, the dynamic similarity exists, when both of them have same lengthscale ratio, time-scale ratio and force-scale (or mass-scale ratio). 4. What is the significance of doing similitude? (20 pts) The importance of similitude comes from its capacity to offer a regulated, affordable method of studying the behavior of large-scale systems without the need for costly, timeconsuming full-scale experiments. Engineers and scientists can examine the behavior of a system under different circumstances and make predictions about how the system will act at full scale by building a scaled model of the system. This is made possible by similitude, which maintains crucial physical relationships between the scaled model and the full-scale system, including the ratio of forces, velocities, and other pertinent properties. Similitude also enables the evaluation of various system designs and alterations without the need for costly and time-consuming full-scale studies. In addition to saving time and money, this can give important insights into how the system behaves. Similitude can also be used to examine physical phenomena that are challenging or impossible to see firsthand, such as the behavior of fluids in turbulent flow.
