We are operating a centrifugal compressor. The gas composition does not change during this excursion. While holding suction pressure and flowrate constant, the inlet temperature rises. What would you expect to happen to the discharge pressure, and why

When the inlet temperature of a centrifugal compressor rises, there are a few factors that can affect the discharge pressure. To understand the expected changes, we can consider two primary factors: gas properties and compressor performance.

1. Gas Properties:
As the temperature increases, the gas molecules gain more energy and move faster, resulting in higher kinetic energy. This increased kinetic energy increases the pressure exerted by the gas particles. This effect is described by the Ideal Gas Law: PV = nRT, where P is pressure, V is volume, n is the number of gas molecules, R is the gas constant, and T is temperature. Therefore, if the number of gas molecules and the volume remain constant, an increase in temperature will result in an increase in pressure.

2. Compressor Performance:
Centrifugal compressors operate based on the relationship between the impeller speed, pressure ratio, and flow rate. The performance of the compressor is influenced by the density and viscosity of the gas.

a. Density: The density of the gas decreases as the temperature increases, according to the Ideal Gas Law. At a constant mass flow rate, lower gas density reduces the compressor's ability to compress the gas, leading to a lower discharge pressure.
b. Viscosity: The viscosity of the gas decreases with higher temperatures, resulting in reduced losses and improved efficiency. This could potentially lead to a moderately higher discharge pressure.

Given these factors, we would expect the following:
- The increase in temperature will raise the kinetic energy of the gas molecules, leading to an increase in pressure according to the gas properties.
- However, the density of the gas will decrease due to the temperature increase, resulting in a reduction in discharge pressure.
- The change in viscosity is less significant compared to the density change, so it won't have a significant impact on the discharge pressure.

Thus, if the gas composition, suction pressure, and flowrate remain constant, the discharge pressure of the centrifugal compressor is expected to decrease due to the decrease in gas density caused by the rising inlet temperature.