Question

A stream of air at 35°c and a gauge pressure of 0.5 atm (stream 1) flows into a pipe passing through a heater, emerges at 87°c and 0.2 atm (gauge), and splits into two streams. stream 2 passes out of the system, and stream 3 goes through another heater and emerges at 180°c and 0.1 atm (gauge). flowmeters mounted in all three streams show readings of 3120 l/min (stream 1), 1940 l/min (stream 2), and 3420 l/min (stream 3) Show that the system is not fuctioning properly.

Answer 1

The system is not functioning properly because the flow rates do not match the conservation of mass principle and gauge pressures show inconsistencies. Stream 1's flow rate is not equal to the combined flow rates of streams 2 and 3, indicating a mass balance issue.

Step-by-step explanation:

To determine if the system is functioning properly, we need to consider the principle of conservation of mass, which states that mass cannot be created or destroyed in an isolated system. The mass flow rate in stream 1 should equal the mass flow rates in streams 2 and 3 combined if the system is functioning properly. However, in the given scenario, the flow rates for streams 1, 2, and 3 are 3120 l/min, 1940 l/min, and 3420 l/min respectively. This indicates an inconsistency since the sum of stream 2 and stream 3's flow rates (1940 l/min + 3420 l/min) does not match the flow rate of stream 1 (3120 l/min).

Moreover, the gauge pressures also show an inconsistency. Typically, in a closed system, pressure losses are expected due to factors such as friction, but the pressure does not miraculously increase as it seems to do between stream 2 and stream 3 (from 0.2 atm to 0.1 atm gauge), which suggests an issue with the system. Additionally, the temperatures of the streams can affect the densities of the air, and thus the mass flow rates, which are not given but could contribute to the discrepancy.