A bearing moves without impediment along a surface by expelling oil of constant density (p=862). The...

 

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A bearing moves without impediment along a surface by expelling oil of constant density (p=862). The system is detailed in Figure 3. You can assume that bearing operates in a steady condition as the oil tank slowly empties. The bearing inlet (A) has dimensions of D = 2.5cm and the bearing outlet (42) has dimensions of D = 12.5cm. The tank is defined by dimensions of height (H = 95cm), width (W = 15cm), and length (L= 15cm). The oil exits the tank out of the bottom through an orifice with the same dimensions as the bearing inlet. Assume the change in vertical difference between the tank orifice and the bearing inlet is negligible. The velocity at which it exits the tank can be modeled by Utank = 2 xgx htank where htank is the height of the oil in the reservoir. While the bearing is in steady operation, it is lifted off the surface at height h. Hint: You find it helpful to ues multiple control volumes to model the different subsystems of the Tank and Bearing Answer the following questions: (a) How far is the bearing lifted from the ground during operation when the tank is full if the radial velocity (vr) is 110% of the velocity of the bearing outlet? (b) In order for the bearing to operate properly, there needs to be a minimum clearance of hmin = 0.75cm. How much oil is left in the tank at this point in (kg)? Assume after the oil level drops below the full condition in part a), the radial velocity (v.) becomes constant at 0.2m/s. General information H W Tank h A Bearing A Figure 3: Oil Reservoir and Bearing system Critical pressure for air is P = 3.77 106 Pa, and critical temperature is T = 132.4 K Use specific heat ratio of y = 1.4 where needed. Use gravitational acceleration of g = 9.8m/s Compressibility chart can be found in the slides, available on Canvas A bearing moves without impediment along a surface by expelling oil of constant density (p=862). The system is detailed in Figure 3. You can assume that bearing operates in a steady condition as the oil tank slowly empties. The bearing inlet (A) has dimensions of D = 2.5cm and the bearing outlet (42) has dimensions of D = 12.5cm. The tank is defined by dimensions of height (H = 95cm), width (W = 15cm), and length (L= 15cm). The oil exits the tank out of the bottom through an orifice with the same dimensions as the bearing inlet. Assume the change in vertical difference between the tank orifice and the bearing inlet is negligible. The velocity at which it exits the tank can be modeled by Utank = 2 xgx htank where htank is the height of the oil in the reservoir. While the bearing is in steady operation, it is lifted off the surface at height h. Hint: You find it helpful to ues multiple control volumes to model the different subsystems of the Tank and Bearing Answer the following questions: (a) How far is the bearing lifted from the ground during operation when the tank is full if the radial velocity (vr) is 110% of the velocity of the bearing outlet? (b) In order for the bearing to operate properly, there needs to be a minimum clearance of hmin = 0.75cm. How much oil is left in the tank at this point in (kg)? Assume after the oil level drops below the full condition in part a), the radial velocity (v.) becomes constant at 0.2m/s. General information H W Tank h A Bearing A Figure 3: Oil Reservoir and Bearing system Critical pressure for air is P = 3.77 106 Pa, and critical temperature is T = 132.4 K Use specific heat ratio of y = 1.4 where needed. Use gravitational acceleration of g = 9.8m/s Compressibility chart can be found in the slides, available on Canvas