Adiabatic compressible flow

FIG, 6"22 Adiabatic compressible flow in a pipe with a well-rounded entrance. 

Lawlb. C. . Trans. Am. Inst. Chem. Eng. 39 (1948) 385. Isothermal and adiabatic flow of compressible fluids. 

The work for a real adiabatic compression can also be calculated from the difference between the total enthalpy of the outlet and inlet flows ... 

The mass flow rate under adiabatic conditions is always somewhat greater than that under isothermal conditions, but the difference is normally <20%. In fact, for long piping systems (L/D > 1000), the difference is usually less than 5% (see, e.g., Holland, 1973). The flow of compressible (as well as incompressible) fluids through nozzles and orifices will be considered in the following chapter on flow-measuring devices. 

Originally Bowden s school suggested that heat from the adiabatic compression of such gas bubbles initiated explosion in the surrounding liquid. Johansson coworkers (Ref 4), however, pointed out that heat flow from a compressed gas bubble to the surrounding liquid is much too slow to account for the observed phenomena, particularly at low impact energies. They have shown that to achieve explosion fine droplets... 

So far, we have limited our discussion to adiabatic compression efficiency. This sort of inefficiency downgrades work to heat. For a given compression ratio, the temperature rise of the gas as it flows through the compressor may be excessive, thus indicating a low adiabatic compression efficiency. Both centrifugal and reciprocating compressors suffer from this common problem, which is the subject of Chap. 30. 

Volumetric efficiency applies only to reciprocating compressors. A reduction in volumetric efficiency reduces the gas flow through the compressor. A reduction in volumetric efficiency need not reduce the adiabatic compression efficiency. 

Rapid aerodynamic flow past obstacles involves adiabatic compressions and rarefactions, and is influenced by relaxation of internal degrees of freedom in a way similar to shock phenomena. This effect has been quantitatively treated by Kan-trowitz18, who developed a method for obtaining relaxation times by measuring the pressure developed in a small Pitot tube which forms an obstacle in a rapid gas stream. This impact tube is not a very accurate technique, and requires a very large amount of gas it has been used to obtain a vibrational relaxation time for steam. 

This is the compressibility usually employed sometimes, as in considering sound waves, we require the adiabatic compressibility, the fractional decrease of volume per unit increase of pressure, when no heat flows in or out. If there is no heat flow, the entropy is unchanged, in a reversible process, so that an adiabatic process is one at constant entropy. Then we have... 

The gas is cooled before it enters the compressor to a temperature such that the exit gas from the compressor will be at 450°F and 360 psia assuming ideal adiabatic compression. To get the compressor entering-gas flow rate, assume that pxv - p2v. Neglect pressure drop due to the cooler. 

Duct Flow of Compressible Fluids Thermodynamics provides equations interrelating pressure changes, velocity, duct cross-sectional area, enthalpy, entropy, and specific volume within a flowing stream. Considered ere is the adiabatic, steady-state, one-dimensional flow of a compressible fluid in the absence of shaft work and changes in potential energy. The appropriate energy balance is Eq. (4-155). With Q, Wj, and Az all set equal to zero,... 

The flow of compressible fluids (e.g., gases and vapors) through pipelines and other restrictions is often affected by changing conditions of pressure, temperature, and physical properties. The densities of gases and vapors vary with temperature and pressure. During isothermal flow, i.e., constant temperature (PV = constant) density varies with pressure. Conversely, in adiabatic flow, i.e., no heat loss (PV " = constant), a decrease in temperature occurs when pressure decreases, resulting in a density increase. At high pressures and temperatures, the compressibility factor can be less than unity, which results in an increase in the fluid density. 

First note the phrase of itself —heat cannot of itself pass fiom a low to a high temperature We have seen that by means of an adiabatic compression of a system the temperature rises, heat being evidently thereby carried up the temperature scale But this does not contradict the above statement about the natural flow of heat, for we have, by the aid of external agency, had to do work, namely, to compress the system m order to make the temperature rise It is a known experimental fact that systems, say gases, naturally tend to expand, the molecules tend to fly apai t and not to contract This fact is evidence, of a molecular... 

A 0.6 m diameter gas pipeline is being used for the long-distance transport of natural gas. Just past a pumping station, the gas is found to be at a temperature of 25°C and a pressure of 3.0 MPa. The mass flow rate is 125 kg/s, and the gas flow is adiabatic. Forty miles down the pipeline is another pumping station. At this point the pressure is found to be 2.0 MPa. At the pumping station the gas is first adiabatically compressed to a pressure of 3.0 MPa and then isobar-ically (i.e., at constant pressure) cooled to 25°C. 

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