Prove that $V_r = V_{e.r}$

$V_c = V_f × r_c$

Mumbai University > Mechanical Engineering > Sem 4 > Production Process II

Marks: 5M

Year: Dec 2015

We know by sine rule; $\frac{V_c}{sin\big[ 90 - (\phi - \alpha)\big]} = \frac{V_f}{sin \phi} = \frac{V_S}{sin(90 - \alpha)}$

Also $r_c = \frac{t_2}{t_1} = {cos(\phi - \alpha)}$

using; $\frac{V_c}{sin\big[90 - (\phi - \alpha)\big]} = \frac{v_f}{sin \phi}$

Therefore, $V_c = \frac{V_f}{sin \phi} × sin [90 - (\phi - \alpha)]$ $\hspace{1cm}$ $\text{but} \ sin [90 - (\phi - \alpha) = cos(\phi - \alpha)$

Therefore $V_c = V_f × r_c$

Hence proved.