Answer to Question #98651 in Mechanical Engineering for Noah

Question

A hydrostatic bearing is used to rotate a load. The load 500kN, fluid viscosity 500 mPa-s. The bearing has an outside diameter of 500mm and an inside diameter of 400mm.

a) What flow Q is required if the film thickness is 1mm?
b) What Pressure is required?
c) what is the friction torque if it is rotated at 3 rad/s?

Answer 1

$$Fout=\pi*D^2/4=3.1415*500/4=196343.75$$

$$Fin=\pi*d^2/4=3.1415*400^2/4=125660$$

$$\Delta F=Fout-Fin=70683.75$$

$$Feff=Fin+0.5*\Delta F=125660+0.5*70683.75=161002$$

PRESSURE

$$p=N/Feff=500000N/161002mm^2=3.11MPa$$

FLOW

$$Q=(p*h^3/(12*\rho))*((D-d)/2)*(1/(\pi*D))=3.11MPa*(1mm)^3*(500mm-400mm)/(12*500*10^(-9) MPa*s*2*3.1415*500mm)=16500mm^3/s=0.0165l/s$$

FRICTION TORQUE

$$M=\rho*\Delta F*\omega*(D-d)^2/(h*2*2^2)=500*10^(-9)MPa*s*70684mm^2*3rad/s*(500mm-400mm)^2/(1mm*2*4)=10800N*mm=10.8Nm$$