Oil SG086 enters into a thrust bearing Its volume flow rate

Oil (SG=0.86) enters into a thrust bearing. Its volume flow rate is 0.06 cm3/sec. The bearing is a circular disk, 10 cm in diameter. There is a 2 mm gap between the bearings surfaces. The oil supply pipe is 3mm in diameter. Calculate the average inlet velocity, VI, in units m/sec. Calculate the average radial exit velocity, V2, in units m/sec assuming purely radial flow Calculate the mass flow of the oil through the system in kg/sec.

Solution

Inlet volume flow V = 0.06 cm³/s

Inlet dia = 3mm = 0.3 cm

Area of cross section A = (0.15)² = 0.071 sq.cm

Flow velocity = 0.06/0.071 =0.85 cm/s

                                 = 0.0085 m/s

Circumference of the bearing = 2r = 2**5 cm

The outlet for the oil is the opening area around the circumference

Outlet area = 2rh = 2**5*0.2 sq.cm

                                    = 6.28 sq.cm

Radial velocity = 0.06/6.28 = 0.0096 cm/s

                             = 9.6e-5 m/s

Mass flow = 0.06*0.86 gm/s ( density of water = 1gm/cc)

                     = 0.0516 gm/s

                      = 5.16 e-5 kg/s