# Enter your parameter set number (1-27)

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1 1- Helium balloons fly and balloons with air sink. Assume that we want to get a balloon that is just floating in the air, neither rising nor falling, when a small weight is placed hanging in the balloon. This may be accomplished by mixing air and helium in the right proportions. Assume that the balloon and the weight have a total mass of m (g) and that the balloon is inflated to a volume of V (liter). What is the necessary volume concentration and mass concentration of helium and air in the balloon to make it float? The temperature in the air and in the balloon is T ( C), the ambient air pressure is 1 bar, the pressure in the balloon is 1.05 bar. The molecular weight of air is M air = 29 kg/kmol and for helium M helium = 4 kg/kmol. The general gas constant is J/(kmol K). Acceleration of gravity is 9.81 m/s 2. The mixture can be treated as an ideal gas. Enter your parameter set number (1-27) your answer with 4 decimals.

2 volume concentration of air is volume concentration of helium is mass concentration of air is mass concentration of helium is 2- A cycle consists of three internally reversible processes with a gaseous medium according to following: a-b: Isothermal compression b-c: Heat transfer at constant pressure c-a: Isentropic expansion Compression ratio Va/Vb and κ is given according to your personal number. Calculate thermal efficiency.

3 Enter your parameter set number (1-27) thermal efficiency is % 3- A compressor is used to compress air of the temperature T ( C) from P1 bar to P2 bar. The compressor can be as adiabatic but not isentropic. Measurements show that the compressor work is 350 kj/kg. What is the isentropic thermodynamic efficiency of the compressor and by how many percent would the compressor work decrease if it was possible to arrange an ideal isothermal compression? The air may be treated as an ideal gas with κ=1.4, the molar mass 29 kg/kmol. The value of the general gas constant is J/(kmol K).

4 Enter your parameter set number (1-27) isentropic thermodynamic efficiency is percent would the compressor work decrease is 4- A cycle consists of three internally reversible processes with air as working medium according to following: a-b: Isentropic compression b-c: Heat transfer at constant pressure

5 c-a: Heat is rejected at constant volume Calculate: a) Work and heat transfer for each sub-process (expressed per unit mass) b) Thermal efficiency of the cycle p a ( bar), T a (K) and p b (bar) are given according to your personal data. Assume air as ideal gas with M=29 and κ=1.4 Enter your parameter set number (1-27) Work for a-b is KJ/Kg

6 Work for b-c is KJ/Kg Work for c-a is KJ/Kg Heat for a-b is KJ/Kg Heat for b-c is KJ/Kg Heat for c-a is KJ/Kg Thermal efficiency is % 5- You are asked to help installing a water line from the basement to a new bathroom on the second floor. The elevation difference between the basement and the second floor is H (m). To get from the connection point in the basement to the wash basin in the bathroom you need to install five bends with the loss coefficient ζ =0,3. You also install a valve in the basement with ζ=1. The tap in the wash basin also has ζ=1. The total tube length is 10 m. The available water pressure in the basement is 2 bar (gage). You would like to have a water flow of V (liters per minute). Is it then sufficient to install a tube with d (mm) inner diameter? The kinematic viscosity could be assumed to be m 2 /s and the density to be 1000 kg/m 3. a) Calculate the total pressure drop. b) Is available pressure (2 bar) sufficient to overcome the pressure drop?

7 Enter your parameter set number (1-27) total pressure drop is bar Enter "1" for yes and "0" for no 6- Through a pipe with d 1 =120 mm and L 1 =120 m, water is flowing from reservoir A to ramification at D from where a pipe with d 2 =75 mm and L 2 =60 m leads to reservoir B in which water level is H a-b (m) below reservoir A. Third pipe with d 3 =60 mm and L 3 =40 m connect D to reservoir C with a water level of H a-c (m) under the reservoir A according to the figure. Calculate volume flow (m 3 /kg) in those three pipes if they have same friction coefficient f, which is given from your personal number. Assume

8 other losses negligible and the reservoir are enough large and open to the ambient. Enter your parameter set number (1-27)

9 your answer with 4 decimals. volume flow in 1 is volume flow in 2 is volume flow in 3 is (m 3 /kg) (m 3 /kg) (m 3 /kg) 7- In a large container pressure is P 2 bar. 1. Calculate mass flow of the air (g/s) flowing into the container if an opening is a converging nozzle with an isentropic process 2. Assume that the opening is a converging-diverging nozzle, calculate for isentropic process, required A 2 /A min where sound velocity is occurred and also the mass flow of the air through the nozzle (g/s) A=1 mm 2 for both cases. Ambient air (M=29 and κ=1.4) has a pressure of 1 bar and temperature of T 0 ( C).

10 Enter your parameter set number (1-27) mass flow of the air for part 1 is (g/s) A 2 /A min is mass flow of the air for part 2 is (g/s) 8- Now you are planning to increase the insulation of the house and the question is how thick the insulation should be. You know that the wall at present has a U-value of 0.6 W/(m 2 K). You would like the wall to get a U- value of 0.2 W/(m 2 K) after the additional insulation. The insulation you use has a thermal conductivity of k (W/(m K)). The heat transfer coefficients on the outside (h out ) and inside (h in ) are given from your personal number.

11 Enter your parameter set number (1-27) The insulation is cm 9- Steel balls at diameter D meter are annealed by heating to Ti and then slowly cooling to 400 K in an air environment for which T=325 K and at given heat transfer coefficient of h. Assuming the properties of the steel to be k=40 W/m.K, density=7800 kg/m 3, and Cp=600 J/kg.K. Estimate the time required for the cooling process. (Negligible radiaition effects and constant properties)

12 Enter your parameter set number (1-27) time is s 10- Two large parallel planes having emissivities of epsilon 1 and epsilon 3 are maintained at temperatures of T1 (K) and T3 (K), respectively. A radiation shield having an emissivity of epsilon 2 on both sides is placed between the two planes. Calculate: 1- the heat transfer rate per unit area if the shield were not present. 2- the heat transfer rate per unit area with the shield present.

13 3- the temperature of the shield. Enter your parameter set number (1-27) heat transfer rate per unit area without shield is W/m 2 heat transfer rate per unit area with shield is W/m 2 the temperature of the shield K

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