Channel friction

Osmotic Pinch As the feed travels along the feed channels, friction losses lower the feed pressure. Solvent flux along the feed channel dewaters the feed and increases solute concentration and osmotic pressure. For a recovery or conversion ratio CR, a module solute retention R, and an inlet solute concentration of c , the bulk concentration cj, is... 

Pressure gradients in the gas channels are caused by friction to flow in the channels and by variations of gas velocity in the channels. Friction in the channels causes a reduction in pressure in the flow direction, in both the inlet and outlet channels. Since these channels generally have their openings at the opposite ends of a catalyst slab, the pressure gradients in the inlet and outlet channels are in the same direction, and therefore there is some compensating effect in the local driving force for lateral flow through the bed. 

Stainless steel 0.03-0.09 Twelve channel friction and Conforming, flat-on-flat configuration McKellop (1981)... 

Co-Cr-Mo + UHMWPE 0.05-01.1 Twelve channel friction and wear machine FW-12 Conforming, flat-on-flat configuration Velocity = 100 cyc./min Pressure = 6.90 MPa Duration 3.7 x 10 cycles Lub bovine calf serum w/55 sodium azide McKellop (1981)... 

Co-Cr-Mo (passivated) + UHMWPE (HiFax 1900) Machined UHMWPE 3.23 in/in x 10 Molded UHMWPE 1.50 in/in x lO NA m Annular disk on flat pin Range of motion = 110° Sliding velocity = 43.3 in/min Stress = 500 psi Lub Ringer s solution Twelve channel friction and UHMWPE transfer film. Quantification of wear Miller et al (1974)... 

The terms in the sum consist of the channel friction factor Xi and the pressure loss coefficient of channel internals or fittings j. For laminar flow in straight channels, the charmel fnction factor Xi is inversely proportional to the Reynolds number in the charmel ... 

The pressure drop across this model structure (Figure 2.8b) is now balanced with the pressure drop Ap ef through the reference channel. Using Equation (2.4), the pressure drop per unit length can be calculated with the channel friction factor, the hydraulic diameter and the mean velocity... 

Horizontal LAD channel tests show that the frictional and dynamic pressure losses within the channel are quite small. The signals are barely measurable in LH2, and the signals are small for LOX flows in excess of 2.25 kg/s. The ID model correlates with the single set of LOX channel frictional pressure drop data. Disparity is due to higher than expected screen injection velocities at the channel exit and scatter in the data. 

Frictiona.1 Pressure Drop. The frictional pressure drop inside a heat exchanger results when fluid particles move at different velocities because of the presence of stmctural walls such as tubes, shell, channels, etc. It is calculated from a weU-known expression of... 

Vfjp is the friction velocity and =/pVV2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu p/. . The universal velocity profile is vahd in the wall region for any cross-sectional channel shape. For incompressible flow in constant diameter circular pipes, = AP/4L where AP is the pressure drop in length L. In circular pipes, Eq. (6-44) gives a surprisingly good fit to experimental results over the entire cross section of the pipe, even though it is based on assumptions which are vahd only near the pipe wall. 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

The most often used friction correlation for open channel flows is due to Manning (Trans. Inst. Civ. Engrs. Ireland, 20, 161 [1891]) and is equivalent to... 

For friction loss in laminar flow through semicircular ducts, see Masliyah and Nandakumar AlChE J., 25, 478-487 [1979]) for curved channels of square cross section, see Cheng, Lin, and On ]. Fluids Eng., 98, 41-48 [1976]). 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

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