Centre-line

Solution Although the composite wall is curved, the r/h) value is large and so it can be analysed using the method illustrated for laminates. In this case, each ply is isotropic and so the properties do not vary with 6. It is thus necessary to get Q for each ply relative to the centre line of the wall thickness... 

Assuming as before that there are four layers with the centre line at the mid-plane of the cross-section, then... 

Solution This stacking sequence is similar to that in Example 3.11 except that in this case the laminate is not symmetrical. As shown in Fig. 3.27, the centre line of the laminate is in the middle of one of the plies and... 

Also, for the element of fluid of depth, dy, at distance, y, from the centre line (and whose velocity is V) the elemental flow rate, dQ, is given by... 

Fig. 5.23 show the solution to Fourier s equation in terms of the temperature gradient at the centre line of section considered and the Fourier Number for... 

Example 5.11 A polyethylene injection moulding is in the form of a flat sheet 100 mm square and 3 mm thick. If the melt temperature is 230°C, the mould temperature is 30°C and the plastic may be ejected at a centre-line temperature of 90°C, estimate... 

From Fig. S.23 it may be seen that the centre line temperature gradient at this Fourier Number is almost 1. 

A lace of polyethylene is extruded with a diameter of 3 mm and a temperature of 190°C. If its centre-line must be cooled to 70°C before it can be granulated effectively, calculate the required length of the water bath if the water temperature is 20°C. The haul-off speed is 0.4 tn/s and it may be assumed that the heat transfer from the plastic to the water is by conduction only. 

Crystallization Process Systems Centre line Centre line... 

Section through exposed surface (along centre line)... 

The velocity of the liquid varies over the cross-section and is usually a maximum at a depth of between 0.05 D and 0.25 D below the surface, at the centre line of the channel. The velocity distribution may be measured by means of a pitot tube as described in Chapter 6. 

The velocity at the centre line, uCl, is then given by putting r = 0 ... 

Combining equations 3.132 and 3.133, gives the velocity profile in terms of the mean velocity u in place of the centre-line velocity uCL as ... 

Compared with the parabolic profile for a Newtonian fluid (n = 1), the profile is flatter for a shear-thinning fluid ( < 1) and sharper for a shear-thickening fluid (n > l). The ratio of the centre line (uCl) to mean (k) velocity, calculated from equation 3.133, is ... 

The centra] unsheared core in which the fluid is all travelling at the centre-line velocity. 

What will be the pressure drop, when the suspension is flowing under laminar conditions in a pipe 200 m long and 40 mm diameter, when the centre line velocity is 1 m/s, according to the power-law model Calculate the centre-line velocity for this pressure drop for the Bingham-plastic model. 

Figures 9.14-9.16 enable the temperature 9C at the centre of the solid (centre-plane, centre-line or centre-point) to be obtained as a function of the Fourier number, and hence of time, with the reciprocal of the Biot number (Bil) as parameter.

The application to pipe flow is not strictly valid because u (= fRjp) is constant only in regions close to the wall. However, equation 12.34 appears to give a reasonable approximation to velocity profiles for turbulent flow, except near the pipe axis. The errors in this region can be seen from the fact that on differentiation of equation 12.34 and putting y = r, the velocity gradient on the centre line is 2.5u /r instead of zero. 

The flowrate of a fluid in a pipe is measured using a pilot tube which gives a pressure differential equivalent to 40 mm of water when situated at the centre line of the pipe and 22.5 mm of water when midway between the axis and the wall. Show that these readings are consistent with streamline flow in the pipe. 

Distance from duct Manometer Reading centre line (m) (mm)... 

Ancillary equipment attached to a tall vessel will subject the vessel to a bending moment if the centre of gravity of the equipment does not coincide with the centre line of the vessel (Figure 13.21). The moment produced by small fittings, such as ladders, pipes and manways, will be small and can be neglected. That produced by heavy equipment, such as reflux condensers and side platforms, can be significant and should be considered. The moment is given by ... 

L0 = distance between the centre of gravity of the equipment and the column centre line. 

Any horizontal force imposed on the vessel by ancillary equipment, the line of thrust of which does not pass through the centre line of the vessel, will produce a torque on the vessel. Such loads can arise through wind pressure on piping and other attachments. However, the torque will normally be small and usually can be disregarded. The pipe work and the connections for any ancillary equipment will be designed so as not to impose a significant load on the vessel. 

L Distance between centre line of equipment and column L... 

A defect in rubber products where a component has been misaligned in relation to the centre line, e.g., conductor in a cable, breaker strip in a conveyor belt or pneumatic tyre. 

Another feature of meteorites that proves to be important is the calcium-aluminium inclusions (CAIs), which, as the name suggests, show regions of enhanced Ca and Al. These micron- to centimetre-sized particles are some of the oldest objects known and have a similar temperature history. They probably formed at temperatures in the region 1700-2400 K and so are close to the centre line of the solar nebula. Although it is hard to be sure about the origin of these objects, there is agreement on their age based on radioisotope dating. 

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