4.2 Universality of the loss coefficients

Die casting engineers who are not familiar with fluid mechanics ask whether the loss coefficients obtained for other liquids should/could be used for the liquid metal. = 0.4

Figure: The results for the flow in a pipe with orifice

To answer this question, many experiments have been carried out for different liquids flowing in different components in the last 300 years. An example of such experiments is a flow of different liquids in a pipe with an orifice (see Figure ). Different liquids create significant head loss for the same velocity. Moreover, the differences for the different liquids are so significant that the similarity is unclear as shown in Figure . As the results of the past geniuses work, it can be shown that when results are normalized by Reynolds number () instated of the velocity and when the head loss is replaced by the loss coefficient, one obtains that all the lines are collapsed on to a single line as shown in Figure . simplified version of the dimensional analysis. Perhaps to refer to the dim chapter = 0.5

Figure: The results for the flow in a pipe with orifice

This result indicates that the experimental results obtained for one liquid can be used for another liquid metal provided the other liquid is a Newtonian liquid¹. Researchers shown that the liquid metal behaves as Newtonian liquid if the temperature is above the mushy zone temperature. This example is not correct only for this spesific geometry but is correct for all the cases where the results are collapsed into a single line. The parameters which control the problem are found when the results are ``collapsed'' into a single line. It was found that the resistance to the flow for many components can be calculated (or extracted from experimental data) by knowing the number and the geometry of the component. In a way you can think about it as a prof of the dimensional analysis (presented in Chapter ).