The jet velocity due to such a head of water is the same as that acquired by a body falling freely through the height h under gravity viz., V2gh thus 2gh= 2g (9. Each pound of water coming in at the top of the column and discharged at the base with velocity V has lost potential energy gh and gained an equiva lent amount of kinetic energy This is the energy per pound which would be available for use in a water turbine.
The static head of water corresponding to a pressure of 265 lb. per sq. inch would be 610 feet and the velocity due to this head 198 feet per second.
With a fluid of less density, a longer column would be re quired in order to have the same pressure at the base. In other words the same pressure would then correspond to a greater static head. Considering steam at, say, 265 lb. per sq. inch and a temperature of 700° F, the density of the steam is--a, of that of water and it would therefore require at that density a column i6o times the height to give the same pressure, or 16o x 610=97,600 ft. But this is not all. Steam, in contrast with water, is a highly elastic fluid, and the effective head in steam would be even greater than 97,600 ft., because of the expansion in volume which takes place as the pressure falls. During this process, successive decrements of pressure, associated with successively decreased density, contribute increasing amounts to the static head (figure 2c.). As a consequence of the expansion the fluid cools down considerably, and the actual head is therefore the height of a column of steam at varying density (and temperature) ; the pressure at any point of the column is that due to the weight of the steam above it and the density at that point is the density corresponding to such pres sure. Such a column of steam with a pressure at its base of 265 lb. per sq. inch and a pressure at the top of 4 lb. per sq. inch (measured from zero pressure or an absolute vacuum) would have a height of 365,00o feet. (It should be noted that pressures meas ured from zero pressure [or an absolute vacuum] are designated absolute pressures. A pressure below atmospheric is expressed either as an absolute pressure or as a vacuum, by which is meant the defect below atmospheric pressure. Thus if the barometer reading is 30" of mercury then a perfect vacuum would be called a vacuum of 30" of mercury; and a vacuum of, say, 28" of mer cury is less than a perfect vacuum by the pressure corresponding to 2" head of mercury.) This therefore is the value of the effec tive static head of steam when allowed to expand between these pressures.
Thus the static head h of an expanding fluid can be considered as the height of a column of the fluid at its natural density, that is to say, of a density diminishing from the base upwards just in the same manner as the atmospheric pressure decreases with altitude.
Figure (2) is a diagrammatic comparison of the effective static heads above considered, shown as columns of fluid having a pressure of 265 lb. per sq. inch at the base. (a) shows the height of such a column of water, (b) that of a fluid at the uni form density which steam has at 265 lb. per sq. inch pressure, and (c) that for steam at its natural density.
Actually, of course, the head of steam for a steam turbine is not obtained by means of a vertical column, but by generating steam under pressure in a boiler.
This does not alter matters, however, for imagine a steam boiler, generating steam at 265 lb. per sq. inch absolute, to be connected to the base of the column (c) in figure (2). Then evidently the steam will rise up the column, falling gradually in pressure and temperature just as it would do in a turbine, and at an altitude of 365,00o feet it would leave the top of the column as exhaust steam at 21b./in'. absolute (assuming the external at mosphere absent). Where has the energy originally in the high pressure steam gone? Clearly it is in the gravitational potential energy of the steam raised to the top of the column. In whatever manner the head is generated, the stored energy per pound of fluid is the same. This energy, namely Sum — has been calculated for steam from an experimental knowledge of its properties, and is tabulated for the use of engineers : it is, however, usual to express it in heat units instead of mechanical units, the two being strictly equivalent. (See THERMODYNAMICS.) Table I. gives the theoretical values for the velocity attainable by allowing high pressure steam to escape through a suitably shaped orifice or nozzle, to a place at lower pressure.