Pressure frictional term

In considering the flow in a pipe, the differential form of the general energy balance equation 2.54 are used, and the friction term 8F will be written in terms of the energy dissipated per unit mass of fluid for flow through a length d/ of pipe. In the first instance, isothermal flow of an ideal gas is considered and the flowrate is expressed as a function of upstream and downstream pressures. Non-isothermal and adiabatic flow are discussed later. 

Equations 6.11 and 6.12 can be used for the calculation of the fluid velocity and the impact pressure in terms of the static pressure a short distance upstream. The two sections are chosen so that they are sufficiently close together for frictional losses to be negligible. Thus Pi will be approximately equal to the static pressure at both sections and the equations give the relation between the static and impact pressure—and the velocity — at any point in the fluid. 

The frictional pressure gradient is obtained by different correlations described in following sections. In a horizontal flow, (dp/dz)elev = 0, it is an ideal case to perform experiments excluding the term of elevation pressure drop. Because of nonhomogeneity of the slug flow, the acceleration pressure gradient term is different from that shown above it is given in Section 3.5.2.2. 

Mathur and Klinzing (1981) have developed a frictional term to account for the solids pressure drop which is meant for high loading systems (pL= 10 to 50). Their expression for / . is... 

In most cases the kinetic energy term will be negligible compared with the frictional term. This is useful when calculating the pressure drop for a given flow rate because in this case one of the pressures and therefore the corresponding specific volume will be unknown. An approximate calcula-... 

As noted previously, the kinetic energy term is usually negligible compared with the frictional term and this is certainly true when the pressure drop AP = Pi —P2 is small compared with Pi. In this case, equation 6.42 can be approximated by... 

For single-phase flow the momentum balance can be written to give the static pressure drop as the resultant of acceleration, hydrostatic, and wall-friction pressure-drop terms. 

The friction pressure loss term is split into two parts, one for the suction side of the pump, Eg, and, the other for the discharge side of the pump, Ed- Thus, Equation 5.47 becomes, after solving for W. 

The work extracted from the expanding uid (HA-HC), may be utilized to generate electricity, compress gas, or just be dissipated in an ambient blower or oil friction brake (see Section 3.2.2.4). The net result is that as refrigeration is generated across the turbine, less refrigeration is needed from the incoming air and the air compressor discharge pressure can be run at much lower pressures. Cycles termed low-pressure cycles ensued from this development. 

Static force balance over cake yielding the compressive stress in the matrix of particles. The sum of the accumulative frictional drag and body (gravitational or centrifugal) forces per unit of cross-sectional area is called effective pressure, a term first used in soil mechanics. 

Note that the critical pressure ratio, pidPi< depends only on the specific-heat ratio of the gas being passed, V, and the friction term, 4/L/D. 

Figure 8 from [8] presents the total minichannel pressure loss as a function of the inlet Reynolds number. The total pressure loss includes liquid, two-phase, and vapor depending on the boiling stage in the minichannel. The curve behavior is a classical N-shape observed for all the heat fluxes studied. The total minichannel pressure loss is the sum of fluid pressure loss for each zone and arises when the friction term in the... 

Coulomb s friction theory for particles was based on the idea that the traction force divided by the plate area was given by an adhesion pressure K plus a friction term JA where p was the friction coefficient, i.e. 

The local total pressure drop in a two-phase flow channel is given as sum of three separate components a frictional term, an acceleration term, and a static head term. 

The coefficient f depends on the Reynolds number for flow within the tube. In laminar flow, the Hagen-Poiseuille law can be applied. In turbulent flow the Blasius equation is used. The main difficulty is the evaluation of water pressure drop during transition boiling. The pressure drop consists of three components friction (APf), acceleration (APJ and static pressure (APg). In once-through horizontal tubes boiler APg=0. The Lockard-Martinelli formulation is used to estimate the friction term. 

There are several approaches to developing predictive models for pressure drop and energy losses in dilute-phase pneumatic conveying. The German literature, for instance, uses an expression proposed by Barth (1954) that includes a lift term in the horizontal analysis, while the U.S. approach is prone to lump this effect into the frictional term. 

Meanwhile, the pressure drop for Region 2 is the sum of the hydrostatic, frictional, and dynamic pressure drop terms as defined in the steady state ID pressure drop model. Since there is no injection velocity in this region, there is no FTS pressure loss. 

The pressure head term, Ahp, and the elevation head term, -Ah, are constant and independent of the flowrate. The friction term, -hf, in Equation flS.lll depends upon... 

In the present paper, an experimental rig has been adopted to measure the pressure profile along a relief header, including both straight pipe lengths and fittings. The acceleration term has thus been directly calculated from Equation 2, and the resulting friction term, derived from Equation 1, has been compared with some of the most common calculation methods. 

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