Incremental calculation time to discharge an ideal gas

2 Incremental calculation time to discharge an ideal gas from a tank 

Consider the case in which an ideal gas flows from one tank to another tank at a lower pressure through a convergent nozzle. The second tank is assumed to be at a constant pressure. The flow may be assumed to be isentropic so that the mass flow rate is given by equation 6.107. 

As the gas flows from the first tank, to which there is no feed, the pressure P0 falls and consequently so does the flow rate. Thus it takes progressively longer for each unit mass of gas to flow from the tank. In principle, this problem could be treated in a manner similar to that in Section 10.1 however, the complexity of equation 6.108 makes this impracticable. 

A suitable method of calculation is to divide the period of flow into a number of short intervals so that conditions change only slightly during each interval. One method of doing this is to specify the length of each time interval and calculate the mass of gas flowing from the tank in that interval. From this the mass of gas remaining in the tank can be calculated and hence the pressure at the end of the interval determined. Conditions for the next interval can then be calculated from this pressure. 

In Example 10.2, the range of pressure in the supply tank is specified and a more convenient method of calculation is to split the pressure range into a number of increments. After calculating the mass flow rate, the mass remaining in the tank is determined from the pressure at the end of the increment and hence the required time may be determined. A small refinement is to base the flow rate calculation on the mean pressure in the increment rather than on that at the beginning. 

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