PROBLEM $6$: An infinitely wide step bearing is modified to include an axial groove whose depth is

much greater than the film thickness. The inlet and outlet film thieknesses are $h_1$ and $h_2,$ respectively.

The sliding velocity of the slider is U $,$ and the fluid viscosity is $.$ Assuming that pressure remains

constant in the groove:

$($a$)$ Sketch the pressure distribution for this bearing.

$($b$)$ Determine an expression for the loud$-$carrying

capacity in terms of the maximum pressure.

$($c$)$ Determine the critical speed needed for this bearing

to take off from an initial position when $h_2=0,$ assuming

that the load per unit width of this bearing is $W=$

$15\frac{N}{m}m,B_1=B_2=B_3=15mm,$ and $h_1=0\mathrm{.}05mm.$