The three velocities which are of interest are:

1. The velocity of the tool relative to work or The velocity of cutting (V).

2. The velocity of chip, relative to tool or chip flow velocity (Vf).

3. The velocity of chip relative to work or shear velocity (Vs).

From volume continuity:

$b t. V=b \cdot t_{c} \cdot V_{f}$ $\therefore \frac{V_{f}}{v}=\frac{t}{t_{c}}=r_{c}=\frac{\sin \emptyset}{\cos (\emptyset-\gamma)}$

From figure,

$\frac{V_{s}}{\sin (90-\gamma)}=\frac{V}{\sin [90-(\emptyset-\gamma)]}$ $\frac{V_{s}}{\cos \gamma}=\frac{V}{\cos (\emptyset-\gamma)}$ $\frac{V_{s}}{V}=\frac{\cos \gamma}{\cos (\emptyset-\gamma)}$