Question

Refrigerant 22 vapor enters the compressor of a refrigeration system at an absolute pressure of \(.1379 \mathrm{MPa} .{ }^{2}\) A pressure gage at the compressor exit indicates a pressure of \(1.93 \mathrm{MPa}\). \({ }^{2}\) (gage). The atmospheric pressure is \(.1007 \mathrm{MPa}\). \({ }^{2}\) Determine the change in absolute pressure from inlet to exit, in MPa. . and the ratio of exit to inlet pressure.

Short answer

Change in pressure: 1.8928 MPa. Ratio: 14.73

Step-by-step solution

Understand the Problem

The task is to determine the change in absolute pressure from the inlet to the exit of a compressor and the ratio of exit pressure to inlet pressure. This involves both absolute and gauge pressures.

Identify Given Data

The absolute inlet pressure \(P_{inlet} = 0.1379 \text{MPa}\) The gauge pressures: = \(P_{gauge, exit}\) = \(1.93 \text{MPa}\) (gauge) = Atmospheric pressure \(P_{atm}\) = \(0.1007 \text{MPa}\)

Convert Gauge Pressure to Absolute Pressure

Calculate the absolute exit pressure by adding the atmospheric pressure to the gauge pressure: \(P_{exit} = P_{gauge, exit} + P_{atm}\) \(P_{exit} = 1.93 \text{MPa} + 0.1007 \text{MPa} = 2.0307 \text{MPa}\)

Calculate the Change in Absolute Pressure

Subtract the inlet absolute pressure from the exit absolute pressure: \(\text{Change in pressure} = P_{exit} - P_{inlet}\) \(\text{Change in Pressure} = 2.0307 \text{MPa} - 0.1379 \text{MPa} = 1.8928 \text{MPa}\)

Calculate the Ratio of Exit to Inlet Pressure

Divide the exit absolute pressure by the inlet absolute pressure: \(\text{Ratio} = \frac{P_{exit}}{P_{inlet}}\) \(\text{Ratio} = \frac{2.0307 \text{MPa}}{0.1379 \text{MPa}} \text{Ratio} \approx 14.73\)

Key concepts

absolute pressure

Absolute pressure is the total pressure exerted by a fluid, including the atmospheric pressure. It is measured in relation to a perfect vacuum, which has a pressure of zero.
To determine absolute pressure, you add the gauge pressure (the pressure measured by devices subtracting atmospheric pressure) to the atmospheric pressure.
For example, in the problem we're considering, the absolute exit pressure is calculated as follows:

• Gauge pressure at compressor exit = 1.93 MPa
• Atmospheric pressure = 0.1007 MPa
• Absolute exit pressure = 1.93 MPa + 0.1007 MPa = 2.0307 MPa

Absolute pressure is crucial in many engineering applications to understand the true force exerted on components. It helps in accurate calculations and prevents potential failures.

gauge pressure

Gauge pressure is the pressure measurement that is read from a gauge; it is the difference between the absolute pressure and the atmospheric pressure. It does not include atmospheric pressure in its readings.
The formula to convert gauge pressure to absolute pressure is:

• \[P_{abs} = P_{gauge} + P_{atm}\]

For instance, in this problem, we convert the gauge pressure at the exit (1.93 MPa) to absolute pressure:

• Given gauge exit pressure = 1.93 MPa
• Atmospheric pressure = 0.1007 MPa
• Absolute exit pressure = 1.93 MPa + 0.1007 MPa = 2.0307 MPa

This conversion is vital for accurate pressure calculations, as many physical properties are based on absolute pressures rather than gauge pressures.

pressure ratio

The pressure ratio is a key concept in analyzing the performance of compressors and other fluid-handling devices. It is the ratio of the exit pressure to the inlet pressure, providing insight into how much the pressure has been increased by the device.
In our problem, we determine this ratio using absolute pressures:

• Absolute inlet pressure = 0.1379 MPa
• Absolute exit pressure = 2.0307 MPa
• Pressure ratio = \[\frac{P_{exit}}{P_{inlet}} = \frac{2.0307}{0.1379} \text{ which approximately equals 14.73}\]

A high pressure ratio indicates significant compression, which is vital for efficiently operating refrigeration systems and other applications requiring high pressure outputs.

compressor

A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. Compressors are used in various applications, including refrigeration systems, where they compress refrigerant to facilitate heat transfer.
There are different types of compressors, such as piston compressors, rotary screw compressors, and centrifugal compressors, each suited to specific applications based on performance and efficiency needs.
In the example, the compressor takes in refrigerant at an absolute pressure of 0.1379 MPa and compresses it to an absolute pressure of 2.0307 MPa. This increase in pressure is crucial for the refrigeration cycle, as it allows the refrigerant to effectively cool the desired spaces by facilitating the heat exchange process. Understanding compressor performance through parameters such as change in absolute pressure and pressure ratio helps in optimizing system efficiency and performance.