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Example Pipe Flow

These six variables (considering Apfll as a single variable), in = 6. may be expressed in terms of n = 3 fundamental dimensions, i.e. mass, length [Pg.56]

The procedure for obtaining these dimensionless groups is illustrated in Chapter 6 and in many chemical engineering textbooks.1,3 [Pg.57]


Example—Pipe Flow. Consider the pressure drop and horsepower required to pump 3 ft of water per second through a 12 in. (305 mm) diameter cast iron pipe for a distance of one mile (5,280 ft) (1,610 m). [Pg.105]

Figure 24. Example of flow pattern map for air water system in horizontal pipes. Figure 24. Example of flow pattern map for air water system in horizontal pipes.
Example 2-7 Pipe Flow System With Liquid of Specific Gravity Other Than Water... [Pg.99]

As an example, the flow of air at 293 K in a pipe of 25 mm diameter and length 14 m is considered, using the value of 0.0015 for R/pu2 employed in the calculation of the figures in Table 4.1 R/pu2 will, of course, show some variation with Reynolds number, but this effect will be neglected in the following calculation. The variation in flowrate G is examined, for a given upstream pressure of 10 MN/m2, as a function of downstream pressure P2. As the critical value of P /P2 for this case is 3.16 (see Table 4.1), the maximum flowrate will occur at all values of P2 less than 10/3.16 = 3.16 MN/m2. For values of P2 greater than 3.16 MN/m2, equation 4.57 applies ... [Pg.163]

With turbulent channel flow the shear rate near the wall is even higher than with laminar flow. Thus, for example, (du/dy) ju = 0.0395 Re u/D is vaHd for turbulent pipe flow with a hydraulically smooth wall. The conditions in this case are even less favourable for uniform stress on particles, as the layer flowing near the wall (boundary layer thickness 6), in which a substantial change in velocity occurs, decreases with increasing Reynolds number according to 6/D = 25 Re", and is very small. Considering that the channel has to be large in comparison with the particles D >dp,so that there is no interference with flow, e.g. at Re = 2300 and D = 10 dp the related boundary layer thickness becomes only approx. 29% of the particle diameter. It shows that even at Re = 2300 no defined stress can be exerted and therefore channels are not suitable model reactors. [Pg.48]

The first example pertains to forced convection in pipe flow. It is found that the rate of heat transfer between the pipe wall and a fluid flowing (turbulent flow) through the pipe depends on the following factors the average fluid velocity (u) the pipe diameter (d) the... [Pg.328]

In the second example, let the case of forced convective mass transfer in pipe flow be considered. Let it be assumed that the turbulent flow of the fluid, B, through the pipe is accompanied by a gradual dissolution of the material, A, of the pipe wall. Experimental... [Pg.329]

Viscometric flow theories describe how to extract material properties from macroscopic measurements, which are integrated quantities such as the torque or volume flow rate. For example, in pipe flow, the standard measurements are the volume flow rate and the pressure drop. The fundamental difference with spatially resolved measurements is that the local characteristics of the flows are exploited. Here we focus on one such example, steady, pressure driven flow through a tube of circular cross section. The standard assumptions are made, namely, that the flow is uni-directional and axisymmetric, with the axial component of velocity depending on the radius only. The conservation of mass is satisfied exactly and the z component of the conservation of linear momentum reduces to... [Pg.387]

Example 5.7 We have to design a servo-controller for a mixing system. A blue dye for making denim is injected into a stream of water. The injected dye is blended into the pipe flow with the aid of in situ static mixers. A photodetector downstream is used to monitor the dye concentration. The analog output of the detector is... [Pg.98]

Example 2-3 Scale-Up of Pipe Flow. We would like to know the total pressure driving force (AP) required to pump oil (/z = 30 cP, p = 0.85 g/cm3) through a horizontal pipeline with a diameter (D) of 48 in. and a length (L) of 700 mi, at a flow rate (Q) of 1 million barrels per day. The pipe is to be of commercial steel, which has an equivalent roughness (e) of 0.0018 in. To get this information, we want to design a laboratory experiment in which the laboratory model (m) and the full-scale field pipeline (f) are operating under dynamically similar conditions so that measurements of AP in the model can be scaled up directly to find AP in the field. The necessary conditions for dynamic similarity for this system are... [Pg.32]

Both laminar and turbulent pipe flow of highly loaded slurries of fine particles, for example, can often be adequately represented by either of these two models over an appreciable shear rate range, as shown by Darby et al. (1992). [Pg.165]

The term two-phase flow covers an extremely broad range of situations, and it is possible to address only a small portion of this spectrum in one book, let alone one chapter. Two-phase flow includes any combination of two of the three phases solid, liquid, and gas, i.e., solid-liquid, gas-liquid, solid-gas, or liquid-liquid. Also, if both phases are fluids (combinations of liquid and/or gas), either of the phases may be continuous and the other distributed (e.g., gas in liquid or liquid in gas). Furthermore, the mass ratio of the two phases may be fixed or variable throughout the system. Examples of the former are nonvolatile liquids with solids or noncondensable gases, whereas examples of the latter are flashing liquids, soluble solids in liquids, partly miscible liquids in liquids, etc. In addition, in pipe flows the two phases may be uniformly distributed over the cross section (i.e., homogeneous) or they may be separated, and the conditions under which these states prevail are different for horizontal flow than for vertical flow. [Pg.443]

In some problems it is advantageous to eliminate obvious dependent variables to reduce the number of equations that must be included as constraints. You can eliminate linear constraints via direct substitution, leaving only the nonlinear constraints, but the resulting equations may be too complex for this procedure to have merit. The following example illustrates a pipe flow problem in which substitution leads to one independent variable. [Pg.68]

Since every detail of a plant design must be recorded on paper, many other kinds of drawings also are required for example, electrical flow, piping isometrics, instrument lines, plans and elevations, and individual equipment drawings in all detail. Models and three-dimensional representations by computers also are now standard practice in many design offices. [Pg.20]

Fig. 4. Examples of the behaviour of a polymer thread (c, = 500 ppm, Re = 70000) in turbulent pipe flow. Pictures taken on a high speed camera at a frequency of 1000 exposures per second serve to illustrate this effect (Bewersdorff 1984)... Fig. 4. Examples of the behaviour of a polymer thread (c, = 500 ppm, Re = 70000) in turbulent pipe flow. Pictures taken on a high speed camera at a frequency of 1000 exposures per second serve to illustrate this effect (Bewersdorff 1984)...
Fig. 7. Schematic representation of examples of test geometries used. Open systems channel, rotating disc (Hoyt 1972, 1986). Closed systems pipe flow, couette- or searle-systems (Kulicke 1986)... Fig. 7. Schematic representation of examples of test geometries used. Open systems channel, rotating disc (Hoyt 1972, 1986). Closed systems pipe flow, couette- or searle-systems (Kulicke 1986)...
Example 11.2 Use Eq. (11.17) to derive a general expression for the acceleration length for dilute gas-solid pipe flows. Assume that the Stokes drag coefficient can be used. The friction coefficient of particles at the wall can be estimated by [Konno and Saito, 1969]... [Pg.474]

Example 11.3 Consider a gas-solid horizontal pipe flow. The pipe diameter is 50 mm. The particle used is 50 pm glass bead with the density of 2,500 kg/m3. The average particle volume fraction is 0.1 percent. The gas density and kinematic viscosity are 1.2 kg/m3 and 1.5 x 10-5m2/s, respectively. Estimate the minimum transport velocity and power consumption per unit length. [Pg.475]

This situation has a number of interesting implications. First, it implies that the pressure gradient for such flows must be a constant, that is, the pressure changes (drops or rises—we do not yet know which) linearly with distance. We can further conclude that, in principle, a moving plate that drags liquid with it, as in this case, may, in principle, generate pressure in the direction of flow and that this pressure will increase linearly with distance, just as pressure drops linearly with distance, in pipe flow, for example. [Pg.49]

Equation (94) provides the means for rearranging all of the theoretical expressions for v) given above into expressions involving the friction factor. For example, when Eq. (75) for Newtonian pipe flow is so rearranged and one eliminates (v) in terms of the Reynolds number, Re = D v)p/fi, one obtains... [Pg.266]

Chemical engineering in general, and fluid flow in particular, utilises many dimensionless groups, which are discussed in more detail in Chapter 6 11 Scale-up in Chemical Engineering . Since we will use a piping system as an example in this chapter, we will now consider the pertinent dimensionless groups for pipe flow. [Pg.56]

Figure 7 Fanning friction factor chart for pipe flow. (M) piping system example (see Section 3.10) Re = 363,000, e/d = 0.0005, cp =... Figure 7 Fanning friction factor chart for pipe flow. (M) piping system example (see Section 3.10) Re = 363,000, e/d = 0.0005, cp =...

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