Flow tube

Table 3. Correlations for Convective Heat-Transfer and Friction Coefficients for Circular Tube Flow ...

The vertical tube (water-cooled) generator consists of two concentric tubes the outer of which is cooled with water and acts as the ground electrode. Feed gas is introduced into the top of the inner stainless steel tube (which serves as the high voltage electrode), exits at the bottom of the outer tube, flows upward through the aimular space (which contains the electric discharge), and emerges at the top of the outer tube into a product gas manifold. 

S s, s Cross-sectional area S for minimum cross-sectional area between rows of tubes, flow normal to tubes 5,, for tube-to-baffle leakage area for one baffle for shell-to-baffle area for one baffle for area for flow through window S, g for gross window area S, for window area occupied by tubes Slope of rotary shell Specific gravity of fluid referred to liquid water m fft... 

When pumping down the draft tube, flow normally makes a more troublefree velocity change to a flow going up the annulus. Since the area of the draft tube is markedly less than the area of the annulus, pumping up the draft tube requires less flow to suspend sohds of a given settling velocity than does pumping down the draft tube. 

A number of streamlines form a stream tube. Flows can enter and leave a stream tube only through the ends. 

The calibration air flows through a thin tube. The probe is placed at the exit of the tube. When the tube is long enough and the tube flow is laminar, the reference velocity for calibration can be calculated from the theoretical, fully developed laminar velocity profile. 

Equation (14.30), whose analytical form was Eqs. (14.64) and (14.65), can be used for determining the free-falling velocity w q in the case that the particles behave like separate particles but due to the great number of random collisions have one free-falling velocity w q. Then Eq. (14.71) gives the correction to calculate the falling velocity in tube flow. 

These conditions are similar to flow through orifices, nozzles, and venturi tubes. Flow through nozzles and venturi devices is limited by the critical pressure ratio, r,. = downstream pressure/upstream pressure at sonic conditions (see Figure 2-38C). 

Tube flow area = 0.223/144 = 0.00155 ftVtube Number of tubes = 0.0934/0.00155 = 30.1 tubes/pass... 

Friction resistance to flow inside tubes, flow rate into tubes (per tube) ... 

A full opening valve or variable orifice should be able to restrict flows of liquid into the bottom of the reboUer so that the instability in the liquid in the column will not be direcdy introduced into the inlet of the reboUer. Generally, the liquid inlet nozzle size should be about 50% in the inlet tube flow cross-section area. A large line is sometimes used, but a restricting provision should be provided to to stabilize operations. 

Values to use for Vj, first drum volume—L, choke-tube length, and S, choke-tube flow area—will depend primarily on physical limitations and the degree of attenuation. Attenuation will be discussed later. Generally, the first drum volume may be sized according to piston displacement and volumetric efficiency considerations with a check of the physical limitations (nonacoustic method previously described) as to the choke-tube length and the pressure drop associated with the choke-tube. If the previously mentioned considerations will meet with design requirements, a further check on band-pass frequencies and the degree of attenuation are in order. 

Forced convection outside tubes Flow across single cylinders... 

When these are close together, most of the simultaneously measured velocities will relate to fluid in the same eddy and the correlation coefficient will be high. When the points are further apart the correlation coefficient will fall because in an appreciable number of the pairs of measurements the two velocities will relate to different eddies. Thus, the distance apart of the measuring stations at which the correlation coefficient becomes very poor is a measure of scale of turbulence. Frequently, different scales of turbulence can be present simultaneously. Thus, when a fluid in a tube flows past an obstacle or suspended particle, eddies may form in the wake of the particles and their size will be of the same order as the size of the particle in addition, there will be larger eddies limited in size only by the diameter of the pipe. 

It is desired to warm an oil of specific heat 2.0 kJ/kg K from 300 to 325 K by passing it through a tubular heat exchanger with metal tubes of inner diameter 10 mm. Along the outside of the tubes flows water, inlet temperature 372 K and oudet temperature 361 K. 

Variable viscosity in laminar tube flows is an example of the coupling of mass, energy, and momentum transport in a reactor design problem of practical significance. Elaborate computer codes are being devised that recognize this... 

J. Gotz, K. Zick 2003, (Local velocity and concentration of the single components in water/oil mixtures monitored by means of MRI flow experiments in steady tube flow), Chem. Eng. Technol. 26 (1), 59-68. 

Velocity images and profiles at several selected heights are shown in Figure 4.3.6, where the noisy points in the images indicate the air space where a liquid signal was not detected. When the fluid is inside the glass pipette, the velocity profile is nearly Poiseuille and a non-slip boundary condition is almost achieved. This is consistent with one of the early tube flow reports that the 0.5% w/v solution of... 

Fig. 4.3.6 Velocity maps and profiles at differ- mark the NMR foldbacks from the stationary ent heights of the Fano column. The dark ring fluid at the inner surface of the fluid reservoir, surrounding the pipe at z= 1.5 mm (larger In the velocity profiles, the solid curves are the white arrow) is due to a layer of stationary fluid calculated Poiseuille profiles in tube flow, adhering to the pipe exterior following the Velocity images are reprinted from Ref. [20], dipping of the pipe into the reservoir at the with permission from Elsevier, start of the experiment. The small white arrows...

The cost of recovery will be reduced if the streams are located conveniently close. The amount of energy that can be recovered will depend on the temperature, flow, heat capacity, and temperature change possible, in each stream. A reasonable temperature driving force must be maintained to keep the exchanger area to a practical size. The most efficient exchanger will be the one in which the shell and tube flows are truly countercurrent. Multiple tube pass exchangers are usually used for practical reasons. With multiple tube passes the flow will be part counter-current and part co-current and temperature crosses can occur, which will reduce the efficiency of heat recovery (see Chapter 12). 

Barnea, D., O. Shoham, Y. Taitel, and A. E. Dukler, 1985, Gas-Liquid Flow in Inclined Tubes Flow Pattern Transitions for Upward Flow, Chem. Eng. Sci. 40(1) 131. (3)... 

You are asked to measure the viscosity of an emulsion, so you use a tube flow viscometer similar to that illustrated in Fig. 3-4, with the container open to the atmosphere. The length of the tube is 10 cm, its diameter is 2mm, and the diameter of the container is 3 in. When the level of the sample is 10 cm above the bottom of the container the emulsion drains through the tube at a rate of 12cm3/min, and when the level is 20 cm the flow rate is 30 cm3/min. The emulsion density is 1.3 g/cm3. 

This result can also be derived by equating the shear stress for a Newtonian fluid, Eq. (6-9), to the expression obtained from the momentum balance for tube flow, Eq. (6-4), and integrating to obtain the velocity profile ... 

Because the shear stress and shear rate can be either positive or negative, the plus/minus sign in Eq. (6-54) is plus in the former case and minus in the latter. For tube flow, because the shear stress and shear rate are both negative, the appropriate form of the model is... 

In Section II.B of Chapter 3, the tube flow viscometer was described in which the viscosity of any fluid with unknown viscous properties could be determined from measurements of the total pressure gradient (— A4>/L) and the volumetric flow rate (Q) in a tube of known dimensions. The viscosity is given by... 

This is known as Stokes flow, and Eq. (11-3) has been found be accurate for flow over a sphere for NRe < 0.1 and to within about 5% for NRe < 1. Note the similarity between Eq. (11-3) and the dimensionless Hagen-Poiseuille equation for laminar tube flow, i.e.,/ = 16/tVRe. 

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