Pressure drop in laminar flow

Correlations for heat transfer and pressure drop in laminar flow are ... 

G. Croce and P. D Agaro, Numerical simulation of roughness effect on microchaimel heat transfer and pressure drop in laminar flow, Journal of Physics D Applied Physics 38, 1518-1530 (2005). 

Larrain and Bonilla conducted theoretical analysis of pressure drop in laminar flow of fluid in a coiled pipe [97]. They extended the series to 14th order and solved by means of computer. Austin and Seader came up with a comprehensive review of previous work and gave a detailed numerical solution in the whole laminar range [98]. Their solution, based on the vorticity field, gave excellent agreement with experiments but it did not yield any understanding of the complex interactions between the different forces. 

For nonisothermal systems a general differential equation of conservation of energy will be considered in Chapter 5. Also in Chapter 7 a general differential equation of continuity for a binary mixture will be derived. The differential-momentum-balance equation to be derived is based on Newton s second law and allows us to determine the way velocity varies with position and time and the pressure drop in laminar flow. The equation of momentum balance can be used for turbulent flow with certain modifications. 

Since the pressure drop in laminar flow for a given mass flow rate varies as (diameter) there is a strong disincentive to nse the 1 micron channels currently being considered for the latter application. Hence the interest centres on the use of multi-layer matrices comprising many sets of 100-200 parallel micron channels. The risk of fouling will also ino-ease with decreasing channel width. 

Under laminar flow conditions, the friction factor,/ is directly proporhonal to viscosity and inversely proportional to the velocity, pipe diameter, and fluid density. The friction factor is independent of pipe roughness in laminar flow because the disturbances caused by surface roughness are quickly damped by viscosity [4]. The pressure drop in laminar flow for a circular horizontal pipe is... 

The grid shown in Fig. 6b was developed by Calis et al. (2001) and consisted of five layers of prismatic cells on the walls of the spheres and tube, and unstructured tetrahedral cells in between. To obtain grid-independent pressure drops under laminar flow they had to restrict the first layer of prismatic cells to be 0.052 mm thick. The thickness then increased for the following four layers. The tetrahedral cells were 0.4mm in size. In their later work (Romkes et al., 2003), which included heat transfer, they had to reduce the size of the first layer of prismatic cells by a factor of three under laminar flow. 

In Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

By using experimental data from a pilot plant constructed to simulate the annular flow of clay suspensions in drilling systems and also date from the literature (Langlinais at all it was possible to extend the results in order to predict the laminar-turbulent transition velocity and the pressure drop in turbulent flow. 

The pressure drop for laminar flow through a fixed bed of particles can be predided by the Carman-Kozeiiy equaflon as ex Messed in the fitllowing form ... 

In order to find flexible and effective solutions for process intensification, the major problem identified previously concerns the pressure drop in small channels. This pressure drop under laminar flow conditions can be related to the production flow rate and geometric dimensions as follows ... 

The Hagen-Poiseuille equation, expressing the pressure drop for laminar flow in an empty conduit, when written in the form of (11.5.1-3), leads to a friction... 

For laminar flow of a Newtonian fluid, scaleup at constant pressure drop is identical to scaleup with geometric similarity. For constant pressure drop in turbulent flow, the reactor diameter increases somewhat faster, than for scaleup with... 

A dimensionless ratio that relates to frictional pressure drop in fluid flow in pips, defined by D-V-p/yL for gasses and Newtonian liquids, where D is the inside pipe diameter, V is the average velocity of the fluid (= flow rate/cross-section), p is the fluid density, and p is the mass-based viscosity [Pa = kg/(m s) in SI units]. When Nile = 2,100—4,000, the character of the flow ranges from streamline (laminar) to turbulent. For Non-Newtonian liquids the criterion for flow transition by the Reynolds number is redefined. For a power-law liquid it becomes ) y-2-n / g j gn-i), g flow-behavior... 

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. 

Pressure drop in catalyst beds is governed by the same principles as in any flow system. Consequently, at very low flow, pressure drop is directly proportional to velocity, and at very high flow, to the square of velocity. These conditions correspond to the laminar and turbulent regimes of the flow. 

Estimation of the pressure-drop The system is designed to work within a given pressure limit thus, one needs a relation giving the pressure-drop in the column (per unit length). Darcy s law gives the relation of AP/L versus the mobile phase velocity u. However, the Kozeny-Carman equation is best adapted for laminar flows as described ... 

The plate heat exchanger, for example, can be used in laminar flow duties, for the evaporation of fluids with relatively high viscosities, for cooling various gases, and for condensing applications where pressure-drop parameters are not excessively restrictive. 

For a power-law fluid in laminar flow at a velocity /. in a pipe of length /. the pressure drop -APL will be given by ... 

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