If : W = weight of steam condensed (lbs. per hour);
Q = weight of cooling water circulated (lbs. per hour);
Ti = inlet temperature (°F.) of cooling water;
To = outlet temperature (°F.) of cooling water;
then
To = Ti + 1050 (W/Q)
It will be understood that for high vacua, low temperature of cooling water (Ti) is more important than copious supply (Q/W). It is advantageous, however, to choose a site yielding plenty of cold water, such as a river or canal side. Otherwise it is often necessary to use cooling towers or spray nozzles. The cooling is by evaporation (= 60 to 80 per cent. of W), cold water replacing that evaporated, and yielding water 75° to 80° F. If Ti = 80° F. and Q/W = 70°, a vacuum of 28.34" is possible, but the 0.34" should be allowed for the partial pressure of the air, determined exactly by the air entering and by the displacement of the air-pump.
Another feature of the modern evaporator is the "heater" or "calorifier," by which the liquor to be evaporated is led in a continuous rapid stream through heated tubes immediately prior to its entry into the first effect. It is the aim of the heater to raise the temperature of the liquor to the temperature of evaporation, and so to avoid this being necessary in the first effect. The heater thus further avoids stewing, ensures steady running, and effectively increases the capacity of a machine.
It is noteworthy that superheated steam is not desirable for working an evaporator. The principle of evaporation by steam is not merely that the temperature of the liquor is raised to boiling point; it is that in the condensation of the heating steam its latent heat is yielded to the liquor being evaporated. To evaporate quickly, therefore, the heating steam must condense rapidly. Hence, as superheated steam has a rate of condensation 20-30 times slower than saturated steam, the latter is much to be preferred. A slight superheating, however, may be justifiable where the steam has any distance to travel before use. It is the fact that it is the latent heat of steam which is mainly utilized which gives steam its great practical advantage over hot non-condensable gases. Steam in condensing yields an enormously greater number of heat units per lb. than hot waste gases. Steam has also the advantage of more constant temperature.
The capacity and efficiency of an evaporator depends upon a good many factors, some of which are worthy of discussion at this point.
The transference of heat and the amount of evaporation are directly proportional to the mean temperature difference between the heating steam and the liquor being evaporated. These temperatures, however, both vary somewhat, the steam losing part of its pressure and temperature as it passes along the heating surface; the liquid generally increases in temperature. The mean difference in temperature, moreover, is not the arithmetic mean between the smallest and largest temperature differences, but is given by the following expressions, which yield results not wide apart:—
If θa = temperature difference at commencement;
θe = " " " end;
and θm = mean temperature difference;
then
This mean temperature difference is in practice usually spoken of as the "temperature head" or "heat drop." It will be clear that this temperature head is increased by using steam at higher pressure (temperature), and by evaporating under reduced pressure. Since most liquids have their boiling points reduced about 40° C. by operating in vacuo, the advantage of the vacuum is apparent. It should be remembered that the temperature head has not the same value in any part of the scale: it has more value higher up the scale, because the steam is denser and more heat units come in contact with a given area in a given time. It must also be remembered that whilst the pressure gauge is a most useful indicator of steam temperature, it is not necessarily accurate. The pressure in the hot space is the sum of the pressures of air and steam, and since the temperature (the important condition) of the hot space depends upon the pressure of the steam, and not on the sum of the pressures, the temperature in a steam space is always rather lower than would be supposed from the pressure indicated by the gauge.
The transference of heat is influenced by the velocity of both the heating fluid and the fluid being heated over the heating surface. The more rapidly each fluid moves, the more rapid is the transference of heat, because a greater number of particles of both fluids are brought to the heating surface in any given time. This is popularly known as the effect of "circulation," and is illustrated by the advantage of stirring a liquid being heated in bulk. In the film evaporators the circulation is through tubes at high speed (up to 2 miles a minute), and the maximum effect in this sense is thus obtained. The increase in heat transference is not directly proportional to the increase in velocity, but in a lower ratio, sometimes approximately the square root of the velocity. In such a case, if either velocity be quadrupled, the heat transference is doubled. Other advantages of high velocity are that the heating steam more readily sweeps away condensed steam from the heating surface, and the high-speed film similarly "scours" away "incrustations" on the interior of the tubes.