We will see in Chapter 7 that the models of many fluid systems involve the square-root function \sqrt{h}, which is nonlinear. Obtain a linear approximation of f (h) = \sqrt{h} valid near h = 9.
The truncated Taylor series for this function is
f (h) = f (h_{r} )+\frac{d(\sqrt{h}) }{dh} \mid_{r} (h−h_{r} )where h_{r} =9. This gives the linear approximation
f (h) =\sqrt{9} +\frac{1}{2} h^{−1/2} \mid_{r} (h−9) =3+\frac{1}{6} (h−9)This equation gives the straight line shown in Figure 1.3.5.