The Pneumatic Despatch Tube System of the Batcheller Pneumatic Tube Co. / Also, Facts and General Information Relating to Pneumatic Despatch Tubes

by Birney C. Batcheller

Fig. 48.
PRESSURE AND VELOCITY CURVES.

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In order to make our ideas and thoughts as clear as possible let us represent them by a diagram, Fig. 48. We will suppose that a tank, A, is kept constantly filled with compressed air at a pressure of ten pounds per square inch, from some source of supply. We will suppose that the pressure of the air in this tank never changes, air being supplied as fast as it flows away. Next, let us assume that a tube eight inches in diameter inside and one mile long (five thousand two hundred and eighty feet) is connected to the tank at one end and left open to the atmosphere at the other. The air will flow in a constant stream from the tank into the atmosphere, for the reason that air is being supplied to the tank as fast as it flows away.

Law of Pressure.

—First, let us consider the pressure of the air at various points in the tube. We will, for convenience, represent the pressure in the tank by a vertical line, D E, ten units in length, since the pressure is ten pounds per square inch. Now let us go to a point on the tube one quarter of a mile (one thousand three hundred and twenty feet) from the tank, drill a hole in the tube, attach a pressure-gauge and measure the pressure of the air at this point. We shall find it to be about 7.91 pounds per square inch; or, 2.09 pounds below the pressure in the tank. We will represent this on our diagram by another vertical line, F G, having a length of 7.91 units. Again let us measure the pressure in the tube at a point one-half a mile (two thousand six hundred and forty feet) from the tank. Here we find it to be about 5.61 pounds per square inch, and we represent it by the vertical line, H I, having 5.61 units of length. We note that the pressure is 4.39 pounds below the pressure in the tank. We are at the middle point of the tube and the pressure has fallen to nearly, but not quite, one-half the pressure in the tank. We will now go to a point three-quarters of a mile (three thousand nine hundred and sixty feet) from the tank, and here the pressure is about 3.01 pounds per square inch. We represent it by the vertical line, J K. Lastly, we measure the pressure very near the end of the tube, one mile from the tank, and find it to be about zero, or the same as the pressure of the atmosphere. All of our measurements have been in pounds above the atmospheric pressure; to express them in absolute pressure, we should add to each the pressure of the atmosphere, which is 14.69 pounds, nearly.

Now we will draw a smooth curve through the tops of all our vertical lines, and we have a curve, E, G, I, K, L, representing the pressure in the tube at every point. It falls gradually from ten pounds to zero, but it does not fall in exact proportion to the distance from the tank. Such a fall of pressure would be represented by the straight dash-line, E, L. The reason why the true pressure-curve is not a straight line, and lies above a straight line, is because air is an elastic fluid and expands, becoming larger in volume as the pressure diminishes. The straight dash-line represents the fall of pressure of an inelastic fluid, like water, when flowing in the tube.

The fall of pressure along the tube is analogous to the fall of level along a flowing stream. In fact, we frequently speak of the descent of a stream as the “head of water” when it is used for power purposes, and we mean by this the pressure the water would exert if it were confined in a pipe. The descent, or change of level, in the bed of a stream is necessary to keep the water flowing against the friction of the banks. The descent of the water imparts energy to overcome the friction. In a similar manner, we must have a fall of pressure along the pneumatic tube to overcome the friction of the air against the interior surface of the tube. We find another analogue in the flow of the electric current along a wire; here there is a fall of potential necessary to overcome the resistance of the wire. Since power has to be expended to compress the air and impart to it its pressure, when this pressure disappears we know that the air must be losing its energy or doing work, and we look to see what becomes of it. In the present case, we find that most of this work is expended in overcoming the friction between the air and the surface of the tube.

Uses of Pressure Curves.

—The pressure curve teaches us many things. Suppose we were to establish stations on this tube at the quarter, half, three-quarter, and mile points; we see at once that intermediate-station or closed receivers, described in the last chapter, must be used at all of the stations except the mile point at the end of the tube, because the pressure in the tube is so high above the pressure of the atmosphere that we could not open the tube to let the carriers come out, but at the end of the tube we could use the open receiver. In designing our sending and receiving apparatus for each station, we look to this pressure curve to tell us the pressure which we shall have on the pistons in our cylinders, and are thereby enabled to make them with proper proportions for the work that they have to do.