Cross-flow velocity calculating

The spacing in the end zones will often be increased to provide more flow area at the inlet and outlet nozzles. The velocity in these zones will then be lower and the heat transfer and pressure drop will be reduced slightly. The effect on pressure drop will be more marked than on heat transfer, and can be estimated by using the actual spacing in the end zone when calculating the cross-flow velocity in those zones. 

To encourage vortex shedding and turbulence on the shell side of a heat exchanger, we must increase the cross-flow velocity. To calculate the cross-flow velocity, we proceed as follows ... 

Divide the volume calculated in step 6 by the area calculated in step 5. This is the cross-flow velocity. 

High Cross-flow of the Continuous Phase Miniplant tests of sieve tray extractors are often performed prior to the final design of a commercial-scale column. The design often is scaled up based on superficial velocities of the dispersed and continuous phases calculated from the volumetric flow rates and the column cross-sectional area. However, in scaling up one must be careful about the cross-flow velocity (V eow) of the continuous phase. A value may be estimated from... 

A 1% by weight albumin (Mol weight 65000 g/mol) solution with a flow rate of 360 liter/hr must be concentrated to 10% by weight in a single-stage process. The gelation concentration of albumin is 200 kg/w . The membranes used do completely retain the albumin. Calculate the required membrane area at a cross-flow velocity of 0,5,1.0 and 5.0 m/s, respectively. The flux can be described by the gel polarization model while the mass transfer coefficient can be described as... 

We can now calculate k. J and A for various cross-flow velocities (see table). 

This example shows that both the membrane area required and the power consumption are lower for the two-stage process. On the other hand, the capital cost will be higher for the two-st e process. Funheimore. by increasing the cross-flow velocity from 1 to 3 m/s. the membrane area is reduced by more than a ctor of twa whereas the energy consumpdon increases by one order of magnimde. These data can be used to calculate the actual process costs, where power consumpdon and membraiK area are important parameters. 

Using Poiseuille s formula, the calculation shows that for concentric-tube nebulizers, with dimension.s similar to those in use for ICP/MS, the reduced pressure arising from the relative linear velocity of gas and liquid causes the sample solution to be pulled from the end of the inner capillary tube. It can be estimated that the rate at which a sample passes through the inner capillary will be about 0.7 ml/min. For cross-flow nebulizers, the flows are similar once the gas and liquid stream intersection has been optimized. 

The average experimental value of the coefficient 0 is 1.7 with a standard deviation (og) of 0.05. Equation (7.160) allows one to calculate the momentum ratio (/rj2/foi) required to extend the length of zone I to the value equal to Xj, given that the distance between the directing nozzles is equal to The graph presented in Fig. 7.56 is plotted according to Eq. (7.160) for and X,2 equal to 6.2. The maximum value of reverse flow velocity (n,, .) was found to be in the cross-section at X equal to Xy... 

Ideally, the axial velocity through the cross-flow unit should be greater than about 4-6 m/s to minimize the boundary layer of particles near the membrane surface. The wax permeate flow from the filter is limited by a control valve actuated by a reactor-level controller. Hence, a constant inventory of slurry is maintained within the SBCR system as long as the superficial gas velocity remains constant. Changes in the gas holdup due to a variable gas velocity are calculated... 

The velocity calculated by dividing the volumetric flow rate by the whole cross-sectional area of the bed is known as the superficial velocity u. The mean velocity within the interstices of the bed is then ub = ule. 

Boundary layer formulation. Many membrane processes are operated in cross-flow mode, in which the pressurised process feed is circulated at high velocity parallel to the surface of the membrane, thus limiting the accumulation of solutes (or particles) on the membrane surface to a layer which is thin compared to the height of the filtration module [2]. The decline in permeate flux due to the hydraulic resistance of this concentrated layer can thus be limited. A boundary layer formulation of the convective diffusion equation can give predictions for concentration polarisation in cross-flow filtration and, therefore, predict the flux for different operating conditions. Interparticle force calculations are used in two ways in this approach. Firstly, they allow the direct calculation of the osmotic pressure at the membrane. This removes the need for difficult and extensive experi-... 

A 3.0-cm-diameter cylinder is subjected to a cross flow of carbon dioxide at 200°C and a pressure of 1 atm. The cylinder is maintained at a constant temperature of 50°C and the carbon dioxide velocity is 40 m/s. Calculate the heat transfer to the cylinder per meter of length. 

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