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FLUID MECHANICS - CASE STUDY SOLUTION


Compressed Tanks


Table: Gas Constants for the Problem
  Gas Constant, R
(kJ/kg-K)
Air 0.2870
Ammonia 0.4882
Carbon Dioxide 0.1889
Helium 2.0771
Hydrogen 4.1243
Nitrogen 0.2968
Oxygen 0.2598
R-12 0.06876
R-134a 0.08149

 

   The conditions of the gases are given as follows:
  Number of
Tanks		 Temperature
(K)		 Absolute Pressure
(MPa)
Oxygen 5 290 1.00
Nitrogen 4 290 0.85
Carbon Dioxide 6 290 1.25

The mass of each gas can be determined by the ideal gas law:

     m = pV/RT

For oxygen, the gas constant R is 0.2598 kJ/kg-K. The mass of the oxygen in a single tank is

     m = (1000)(0.25)/(0.2598)(290)
        = 3.318 kg

For nitrogen, the gas constant R is 0.2968 kJ/kg-K. The mass of the nitrogen in a single tank is

     m = (850)(0.25)/(0.2968)(290)
        = 2.469 kg

For carbon dioxide, the gas constant R is 0.1889 kJ/kg-K. The mass of the carbon dioxide in a single tank is

     m = (1,250)(0.25)/(0.1889)(290) = 5.705 kg

The total weight of the tanks is then given by

Wtotal = weight of empty tanks + weight of gases
          = (15)(5)(9.8) + (5)(3.318)(9.8)
                 + (4)(2.469)(9.8) + (6)(5.705)(9.8)
          = 1,330 N