Suppose that H1(s) and H2(s) are two strictly proper singleinput, single-output transfer functions with controllable statespace realizations (A1, B1, C1) and (A2, B2, C2), respectively. Construct a state-space realization for the parallel interconnection H1(s) H2(s), and use the Popov-Belevitch-Hautus eigenvector test to show that the parallel realization is controllable if and only if A1 and A2 have no common eigenvalues.

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -26°c with a volumetric flow rate of 0.18 m3/s. refrigerant exits at 9 bar, 70°c. changes in kinetic and potential energy from inlet to exit can be ignored. determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kw.

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

Arigid tank contains 10 kg of air at 137 kpa (abs) and 21°c. more air is added to the tank until the pressure and temperature rise to 242 kpa (abs) and 32°c, respectively. determine the amount of air added to the tank. [r-0.287 kj/kg k]