4.15. In fluid mechanics, the stream function y, which is related to the flow rate, is frequently employed for analysis. The distribution of y for a particular problem is obtained as \psi=1.1\left[\exp \left(-y^{1.3}\right)\right] \cos \left(\frac{y^{2}}{3 \pi}\right)+0.9\left[\exp \left(-y^{0.7}\right)\right] \sin \left(\frac{y^{2}}{3 \pi}\right) The velocity V is given by dyldy, and the shear force generated by the flow is proportional to d?y/dy. Compute both these derivative sat y = 0.5, with Ay = 0.2, 0.1, and 0.05. Employ second-order central differences.

Fig: 1

Fig: 2

Fig: 3