Shaft Critical Frequency

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`d_(shaft)` =

in shaft diameter

`E_m` =

psi shaft modulus of elasticity

`rho_m` =

lbm/in^3 density of the shaft material

`L` =

in shaft overall length

`S_b` =

in bearing spacing

`W_e` =

lbs equivalent weight of the impellers at the bottom of the shaft

`omega` =

lbs/in specific weight of the shaft