Junction of two tubes

In the next section we will develop a general expression for the reflection and transmission of a wave at the junction of two tubes and in in the subsequent sections, show how this result can be used to determine the behaviour of the whole system. 

If we consider a single tube k in our model, from Equations 11.6, 11.7 and 11.9 we can state the volume velocity and pressure functions in discrete normalised time and distance as 

Now we consider the junction between a tube k with normahsed length Dk and its neighbouring tube +1, shown in Figime 11.10. As this tube is also uniform, it can also be described by Equations 11.11a and 11.11b. 

Joining two tubes creates a boundary condition at the junction, and it is this junction which determines how the sound propagates as a whole. In considering behaviour at a junction, we can use an important principle of physics which states that pressure and volume velocity caimot change instantaneously anywhere. So despite the sudden change in cross sectional area, the volume velocity and pressure caimot abruptly change, and it follows from this that at the point of the junction the pressure and volume velocity must be equal. Hence 

Using these boundary conditions we can relate the forwards and backwards volume velocity equations of tube k and tube + 1 at the junction. That is, at the end d = Dk) of tube k and the start of tube k+ 1 ( 7 = 0) 

We can substitute these equations into one another and eliminate one of the volume-velocity terms. For example, from Equation (11.12) we know that u [n + Dk] = k+ M + Mi+i[n] -b M [n - Die], which we can substitute into Equation (11.13b) to give an expression for [n]  

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Figure C.2. Junction of two acoustic tubes with different areas.

The k p scheme has been used also for the study of transport across junctions connecting tubes with different diameters through a region sandwiched by a pentagon-heptagon pair [25]. In Junctions systems, the conductance was predicted to exhibit a universal power-law dependence on the ratio of the circumference of two CNTs [26]. An intriguing dependence on the magnetic-field direction was predicted also [27]. These newer topics will be discussed elsewhere. 

It yields a characteristic reaction with bromine. If a few drops are, dissolved in 3 c.c. of glacial acetic acid and a little bromine vapour allowed to pass down the tube, a fine crimson colour forms which rapidly extends to the whole of the liquid and soon changes to violet and then to indigo blue with phosphoric acid, the acetic acid solution gives a rose madder colour at the junction of the liquids, and when the liquids are mixed, the colour changes to crimson and then slowly to violet. Baker and Smith consider that the sesquiterpene contains one double linkage. Semmler considers that it is a mixture of at least two bodies, one a bicyclic and the other a tricyclic sesquiterpene. 

A junction in a transfer tube is useful when two parts of the tube are fixed to the respective dewars. An example of a transfer tube is shown in Fig. 5.8. Figure 5.9 shows a sleeve coupling. Examples of transfer lines are in ref. [27,28],... 

The sample block cell 13 h consists of an aluminum oxide block which can be removed from the base plate. The thermocouples serving for DTA and temperature measurement are reinforced up to the hot junction by ceramic oxide capillary tubes. The sample cell can be mounted in either of two alternative positions, according to the quantity of test substance used. The DTA thermocouples extend into either the large or the small hole. 

The experimental apparatus consists essentially of a narrow vertical glass tube down the inner surface of which one liquid is made to flow, the other liquid emerges from a fine glass tip in the form of a narrow jet down the axis of the tube. The two solutions are connected with calomel electrodes employing potassium chloride or nitrate as junction liquids. The E.M.F. of the cell is measured by means of a sensitive quadrant electrometer. The greatest source of error in the method is the elimination of or the calculation of the exact values of the liquid-liquid junction potentials in the system. For electrolytes which are not very capillary active, the possible error may amount to as much as fifty per cent, of the observed E.M.F. 

To about 15 mg in a test-tube, add 3 drops of phosphoric acid and close the tube with a stopper through which passes a smaller test-tube filled with water, and on the outside of which hangs a drop of lanthanum nitrate solution. Heat in a water-bath for 5 minutes (or if necessary bring slowly to the boil over a flame). Mix the drop of lanthanum nitrate solution with 1 drop of 0.02 N iodine on a white tile, and place 1 drop of dilute ammonia solution at the edge of the mixture. A blue color slowly appears at the junction of the two liquids indicating the presence of an acetyl group. 

A thermocouple consists of two wires of dissimilar metals or alloys insulated from each other by placing them in a two-channel porcelain tube. The wires are welded together at one end (the hot or measuring junction of the thermocouple)... 

Optional devices, such as the in-line filter, can be introduced at the junction of the stopcock and outlet tubing. Two filters in series incorporate extra protection against contamination. If the first is observed to be contaminated, then it can be removed, the second filter replaces it, and a new filter is introduced in-line Close the... 

The industrially important nitration of aromatic compounds in a microreactor using two immiscible liquid phases was demonstrated in different studies using either parallel [220] or segmented flow [221]. In all studies, a PTFE capillary microchannel, connected to an inlet junction, was used in which either segmented or parallel flow can be created. The use of PTFE tubing is desirable as it is commercially available and no complicated microfabrication methods are involved. 

Thermocouples are the most commonly used temperature measuring device in elevated temperature thermal analysis. Thermocouples are made up of two dissimilar metals. If the welded junctions between the two materials are at different temperatures, a current through the loop is generated. This phenomenon can be explained by visualizing electrons in a solid as analogous to a gas in a tube (Figure 2.3). 

Resorcinol test Place a few drops of the test solution in a test-tube add several drops of dilute sulphuric acid and a speck or two of magnesium powder. When the metal has dissolved, add about 0-1 g resorcinol, and shake until dissolved. Cool. Carefully pour down the side of the tube 3-4 ml concentrated sulphuric acid. A blue ring will form at the junction of the two liquids. Upon warming the sulphuric acid layer at the bottom of the tube very gently (CAUTION), the blue colour spreads downwards from the interface and eventually colours the whole of the sulphuric acid layer. 

This is the basis of the ring test99 for nitric acid or nitrates, which usually consists in pouring a cold solution of ferrous sulphate gently down the sides of an inclined test-tube on to a layer of concentrated sulphuric acid, containing the nitrate. Since ferric sulphate yields a red compound, possibly Fe2(S04)3.4N0, with nitric oxide in the presence of concentrated sulphuric acid (see p. 161), the colour of the ring formed at the junction of the two liquids will depend upon whether the nitric oxide compound is formed in the concentrated acid or in the aqueous layer, being brown in the latter, but ruddy in the former. 

The detector consisted of a Wheatstone network of capillary tubes that were drilled out of a high conductivity copper block and was fairly compact. The reference flow of mobile phase and the eluent from the column entered at two opposing junctions of the bridge arms (the center of tube (C)) such that the eluent was contained in one vertical arm (C) and the pure mobile phase in a parallel vertical arms (A) and (B). The increase in pressure at the base of tube (C) due to the presence of solute in (C) applied a pressure to the bottom of tube (A). This caused a flow of gas through the anemometer from tube (A) to tube (B) providing an output that was fed to a recording milliammeter. Subsequently all flows exited from the top and bottom of tube (C). 

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