Using Routh’s stability criterion, answer the following parts: (a) Find how many roots with positive real parts are there for Q(s) = s 3 + s 2 + 20s + 78 = 0. (b) Find the range of K such that Q(s) = s 3 + 3Ks2 + (K + 2)s + 4 has all roots in the left half plane. (Here, K is a design parameter.)

Consider airflow over a flat plate of length l = 1.5 m under conditions for which transition occurs at le = 0.9 m based on the critical reynolds number, re,e = 5 x 10. evaluating the thermophysical properties of air at 400 k, determine the air velocity. (hint: use the tables to find the properties of air)

Steam at a pressure of 100 kpa and a quality of 50% initially fills a rigid vessel having a volume of 0.5 m^3. the steam is then heated, causing the pressure in the vessel to rise to 150 kpa. determine: i. the mass of the steam in the vessel. ii. the temperature and quality of the steam after the heating process. ii the mass of the vapour, mg and liquid, m in the vessel after the heating process. if the steam in the vessel is now further heated, what would the pressure and temperature in the vessel be when all steam has turned into saturated vapour? b. sketch the processes in part (a) and part (b) on p-v and t-v diagrams, indicating clearly the temperatures, pressures and the paths. c. (0.59kg, 111.4°c, 73%, 0.4307kg, 0.1 593kg, 2.11 bar, 121.84°c)

Aspherical thermocouple measurement errors a spherical thermocouple made of constantin transfer coefficient between the gas and the thermocouple is h used to measure the temperature of a gas. the heat 400 w/m2 k. calculate the maximum diameter d of the thermocouple if the thermocouple's measurement error should be w 23 within 5% of the initial temperature difference in 5 seconds. for constantin, k 8920 kg/m3, and c 410 j/kg. k.