## Which real root (smallest, middle, or largest) represents this phase at the highest pressure, and what are the Z values at the specified pressures?

When cubic equations of state give three real roots for Z , usually the smallest root is the liquid root and the largest is the vapor root. However, the Peng-Robinson equation can give real roots at high pressure that differ from this pattern. To study this behavior, tabulate all the roots found for the specified gas and pressures. As the highest pressures are approached at this temperature, is the fluid a liquid or gas? Which real root (smallest, middle, or largest) represents this phase at the highest pressure, and what are the Z values at the specified pressures?

(a) Ethylene at 250 K and 1, 3, 10, 100, 150, 170, 175, and 200 MPa

(b) n-Hexane at 400 K and 0.2, 0.5, 1, 10, 100, 130 and 150 MPa

(c) Argon at 420 K and 0.1, 1, 5, and 10 MPa

### design suitable bearings to support the load for at least 5E8 cycles at 1 200 rpm using deepgroove ball bearings.

The shaft shown in Figure P11-4 was designed in Problem 10-19. For the data in row (a) of Table P11-1, and the corresponding diameter of shaft found in Problem 10-19,….

### Find the minimum film thickness for a long bearing with the following data: 30-mm dia, 130 mm long, 0.0015 clearance ratio, 1 500 rpm, ISO VG 100 oil at 200°F, and supporting a load of 7 kN.

1.       A paper machine processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50-m OD X 22-cm ID X 3.23-m long and is on a simply supported, 22-cm OD, steel….

### Find the minimum film thickness for a bearing with these data: 30-mm dia, 25 mm long, 0.0015 clearance ratio, 1 500 rpm, ON = 30, ISO VG 220 oil at 200°F.

1.       Problem 7-12 estimated the volume of adhesive wear to expect from a steel shaft of 40 mm dia rotating at 250 rpm for 10 years in a plain bronze….