Hydraulics — compressible fluids

In case a compressible fluid is flowing from point 1 to point 2, the general equation of flow under steady state can be given by  

Because e + p/p may be written as specific enthalpy h, and as points 1 and 2 were arbitrarily chosen. Equation 2.59 can be expressed as 

---

OTHER COMMENTS used as a solvent for nitrocellulose, cellulose acetate, celluloid, vanous oils, fats, resins, waxes, dyes, tars, lacquers, and eoating compositions used as a preservative in pharmaceutical preparations utilized in some antifreeze solutions, in hydraulic compression fluids, and in metal-cleaning compounds useful as a stripping agent and as a laboratory reagent. 

The hydraulic jump may be compared with the shock wave for the flow of a compressible fluid, discussed in Chapter 4. 

The problems of micro-hydrodynamics were considered in different contexts (1) drag in micro-channels with a hydraulic diameter from 10 m to 10 m at laminar, transient and turbulent single-phase flows, (2) heat transfer in liquid and gas flows in small channels, and (3) two-phase flow in adiabatic and heated microchannels. The smdies performed in these directions encompass a vast class of problems related to flow of incompressible and compressible fluids in regular and irregular micro-channels under adiabatic conditions, heat transfer, as well as phase change. 

The principal use of the plant is lor the oil contained in the seeds, This oil is pressed out without healing the seeds. The particular properties make this oil valuable for specialized uses, such as low temperature lubrication. It is an important constituent of hydraulic brake fluid and other fluids where the degree of compressibility is important- Castor oil also finds medical uses, as an ingredient of special soaps, and in the preparation of some lexiile dyes. Ricin, an alkaloid present in castor oil. also has been used in insecticides. Prior lo the preparation of refined castor oil for medical purposes, ricin must be removed. 

Pitot tube. When a pitot tube is used for the measurement of the velocity of a compressible fluid, the usual hydraulic formula may be employed for all velocities less than about one-fifth that of the acoustic velocity in the medium. The error at this arbitrary limit is about 1%. For higher velocities a correction should be made, which applies up to a Mach number of 1. 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considered incompressible, except for certain calculations involved in hydraulic transient analysis (see following) where compressibility effects are important even for nearly incompressible liquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compressible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (Gas Dynamics, vol. I and II, Wiley, New York [1976]). 

Compressible and Incompressible Flow An incompressible flow is one in which the density of the fluid is constant or nearly constant. Liquid flows are normally treated as incompressible, except in the context of hydraulic transients (see followiM). Compressible fluids, such as gases, may undergo incompressible flow if pressure and/or temperature changes are small enough to render density changes insignificant. Frequently, compressible flows are regarded as flows in which the density varies by more than 5 to 10 percent. 

The pressure drop during the passage of a fluid through a reactor is an important parameter related to the optimization of the energy consumption. Pressure drop will be considered assuming non-compressible fluids and taking the standard assumption of continuum mechanics. Gas properties at temperatures up to 600 K and at a minimum pressure of 0.1 MPa will be used. Fluid velocities less than 10 m s will be considered in channels with hydraulic diameters less than 1 mm. Under these conditions, the fluid flow is laminar and compressibility effects can be neglected [10]. 

A program for hydraulic calculations, hydraulics.exe, has been developed to estimate pressure drop for noncompressible fluids, compressible fluids, and two-phase fluids. The main form has been divided into a number of frames for input and results. Calculations can be performed using either SI or English units (SI unit by default). The units are fixed ones, and the program does not allow for change of individual units. 

The silicone oils and silicone resins find application as (i) lubricants (their change of viscosity with temperature is small), (ii) hydraulic fluids (they are unusually compressible), (iii) dielectric fluids, (iv) for the pro duction of water-repellant surfaces, and (v) in the electrical industry (because of their high insulating properties). 

The hydraulic jar again uses a direct mechanical impact blow. The hydraulic fluid in this tool acts mainly to provide a delay while the desired derrick pull is achieved prior to actuation of the tool. Such tools may also be operated by compressed gas in a closed chamber. The compressed gas can be used to drive a hammer within the jar that strikes the top of a tool anvil. 

A hydraulic system must have a reserve of fluid in addition to that contained in the pumps, actuators, pipes and other components of the system. This reserve fluid must be readily available to make up losses of fluid from the system, to make up for compression of fluid under pressure, and to compensate for the loss of volume as the fluid cools. This extra fluid is contained in a tank usually called a reservoir. A reservoir may sometimes be referred to as a sump tank, service tank, operating tank, supply tank or base tank. 

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

---