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  3. the adjacent rigid cylindrical tank of diameter d20cm and length...

Question: the adjacent rigid cylindrical tank of diameter d20cm and length...

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The adjacent rigid cylindrical tank of diameter D-20cm and length, L-10cm contains 100gm (grams) of air, the pressure, p of which obeys the following function of temperature, T and specific volume, u: where R,a, andb are positive constants. (Recall that p(T,v) denotes that p is a function of the two variables, T and v.) a) What are the base dimensions of the constants R, a and b? b) Given a-163 in SI units and b-1.267cm/gm what is the value of R in SI units if p-20.243bar when the temperature, T-45.67 ? Also calculate the value of R in J/kg/K. [10] [10] [20] c) Determine the values of a and R in US customary units. d) How much mass needs to be added to the rigid tank to raise the gas pressure to 40atm at the same temperature of T--45.67°F? e) What are the base dimensions of the product pu? Calculate the product pu at 200K and 0.01m/kg in J/kg and the equivalent US customary units. f) The tank is emptied and refilled such that the temperature is uniform at 300K, but the gas pressure is not uniform. It is refilled with air such that the pressure varies with radius r (r is a variable, it varies from 0(center of the tank) to D/2 (wall of the tank)) according to where p/ 10atm. Under these conditions the constants a-b-0 from equation (i). Calculate the total air mass inside the tank. [10]g) The circular disk/tank is subjected to a vertical air jet that supports it in such manner as to remain suspended in the air motionless, as shown by the adjacent sketch. The total pressure due to air stream at the bottom surface of the disk is uniform at pB 101400Pa while the pressure at the top surface is not uniform and given by the following function where k is a constant. (Notation: exp(r)-e ) What are the base dimensions of the constant k? Calculate its value based on the condition that the pressure of the air stream at the edge of the disk has to be recovered, i.e. the pressure Air Stream at r D/2 should be pB [10] h) Using plotting software (e.g. excel, MatLab) plot the pressure pf(r) (in bar) vs 2r/D for the given range, i.e. 0srsD/2 . The minimum point of the ordinate should be 0.8bar. [5] i) Calculate the total mass (in lb) of the circular disk. (Newtons lst Law is very useful in this stationary scenario.) 110]

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