A Bourdon gage (see Fig. 2.13) is often used to measure pressure. One way to calibrate this type of gage is to use the arrangement shown in Fig. P2.70a. The container is filled with a liquid and a weight, \(\mathscr{W}\), placed on one side with the gage on the other side. The weight acting on the liquid through a 0.4-in.-diameter opening creates a pressure that is transmitted to the gage. This arrangement, with a series of weights, can be used to determine what a change in the dial movement, \(\theta\), in Fig. P2.70b, corresponds to in terms of a change in pressure. For a particular gage, some data are given below. Based on a plot of these data, determine the relationship between \(\theta\) and the pressure, \(p\), where \(p\) is measured in psi.

Figure P2.70

Fig. 2.13

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W (lb) 0 1.04 2.00 3.23 4.05 5.24 6.31 0 (deg.) 0 20 40 60 80 100 120