Characteristics of Incompressible Flow to Fluid Mechanics Solutions

Characteristics of Incompressible Flow

         Although there is no such thing in reality as an incompressible fluid, this term is applied to liquids. Yet sound waves, which are really pressure waves, travel through liquids. This is an evidence of the elasticity of liquids. In problems involving water hammer, it is necessary to consider the compressibility of the liquid. The compressibility of a liquid is expressed by its bulk modulus of elasticity which influences the wave speed in the liquid. 

         It should be explained here that when density changes of compressible fluids (gases or steam) are gradual and do not change by more than about 10 percent, the flow may be treated as incompressible with the use of an average density. Bernoulli’s equation is a special case of  applied to nonviscous, incompressible fluids (ideal fluid) which do not exchange shaft work with surroundings:

            In real flow systems, however, the Bernoulli equation must be suplemented by a frictional head loss Hf (expressed in feet of a column of the fluid) and by a pumphead term Hp (total dynamic head, TDH, expressed in feet of a column of fluid). Then, for real systems the following is found:

        

      Expressions for calculating the loss of pressure in turbulent flow are based upon experimental data. An empirical transition function for commercial pipes for the region between smooth pipes and the absolute roughness , expressed in feet (millimeters), is used as a measure of pipe wall irregularities of commercial pipes. Formula is the basis for the Moody diagram in the ‘‘transition zone’’ flow. The Moody diagram is widely accepted for hand calculations. For computerized calculations of the pressure drop, however, the Colebrook equation is built into the software.

            Pressure losses which occur in piping systems due to bends, elbows, joints, valves, and so forth are called form losses. Recommended values of local flow resistance coefficients (K-factors) may be found losses may also be expressed in terms of the equivalent length Le of pipe that has the same pressurehead loss for the same flow rate:

*Note : After solving for Le.