Question 3.116: Reconsider Prob. 3-115. Using EES (or other) software, inves......
Reconsider Prob. 3-115. Using EES (or other) software, investigate the effect of the environment temperature on the average air temperature in the balloon when the balloon is suspended in the air. Assume the environment temperature varies from -10 to 30°C. Plot the average air temperature in the balloon versus the environment temperature, and discuss the results. Investigate how the number of people carried affects the temperature of the air in the balloon.
EES Problem 3-115 is to be reconsidered. The effect of the environment temperature on the average air temperature in the balloon when the balloon is suspended in the air is to be investigated as the environment temperature varies from -10°C to 30°C. The average air temperature in the balloon is to be plotted versus the environment temperature.
Analysis The problem is solved using EES, and the solution is given below
| “Given Data:” “atm—atmosphere about balloon” “gas—heated air inside balloon” g=9.807 [m/s^2] d_balloon=20 [m] m_cage = 80 [kg] m_1person=65 [kg] NoPeople = 6 {T_atm_Celsius = 15 [C]} T_atm =T_atm_Celsius+273 “[K]” P_atm = 90 [kPa] R=0.287 [kJ/kg-K] P_gas = P_atm T_gas_Celsius=T_gas – 273 “[C]” “Calculated values:” P_atm= rho_atm*R*T_atm “rho_atm = density of air outside balloon” P_gas= rho_gas*R*T_gas “rho_gas = density of gas inside balloon” r_balloon=d_balloon/2 V_balloon=4*pi*r_balloon^3/3 m_people=NoPeople*m_1person m_gas=rho_gas*V_balloon m_total=m_gas+m_people+m_cage “The total weight of balloon, people, and cage is:” W_total=m_total*g “The buoyancy force acting on the balloon, F_b, is equal to the weight of the air displaced by the balloon.” F_b=rho_atm*V_balloon*g “From the free body diagram of the balloon, the balancing vertical forces must equal the product of the total mass and the vertical acceleration:” F_b- W_total=m_total*a_up a_up = 0 “The balloon is hanging still in the air” |
| \mathrm{T}_ \text{atm.Celcius} [C] | \mathrm{T}_ \text{gas,Celcius} [C] |
| -10 | 17.32 |
| -5 | 23.42 |
| 0 | 29.55 |
| 5 | 35.71 |
| 10 | 41.89 |
| 15 | 48.09 |
| 20 | 54.31 |
| 25 | 60.57 |
| 30 | 66.84 |