ABSTRACT

In describing the behavior of a single lump, we will apply conservation of mass and also Newton's law. During a time interval dt, the difference between mass flo\'/ into and out of a lump must equal the additional mass stored in that lump. Also, the force (pressure times area) difference between left and right ends of a lump must equal the lump mass times its acceleration. In applying conservation of mass, we will need to use the fluid property called the bulk modulus, which is a measure of the fluid's compressibility. As with most material properties, the numerical value of bulk modulus is found by experiment. In this case we compress a fluid sample of volume V and measure the volume change ~ V caused by a pressure change ~P:

isothermal bulk modulus when the process is slow enough to allow the available heat transfer processes to maintain a roughly constant absolute temperature. For rapid processes, there is not enough time for much heat transfer to take place, and we use the adiabatic modulus. For liquids, we often assume the bulk modulus to be independent of pressure, a typical value for hydraulic oil being about 250,000 psi.