# GATE Mechanical 2022 Set 2 | Question: 48

A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross sectional dimensions of this $L$-section bar are shown in the figure. The total extrusion pressure $(p)$ in $\text{MPa}$ for the above process is related to extrusion ratio $(r)$ as

$$p = K_{s}\sigma _{m}\left [ 0.8 + 1.5\: \ln \left ( r \right ) + \frac{2l}{d_{0}}\right ],$$

where $\sigma_{m}$ is the mean flow strength of the billet material in $\text{MPa}$, $l$ is the portion of the billet length remaining to be extruded in $\text{mm}$, $d_{0}$ is the initial diameter of the  billet in $\text{mm}$, and $K_{s}$ is the die shape factor.

If the mean flow strength of the billet material is $50$ $\text{MPa}$ and the die shape factor is $1.05$, then the maximum force required at the start of extrusion is ________________ $\text{kN}$ (round off to one decimal place).

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