above the water in the reservoir, and when the barometer stands at 28 inches. In this case, a = 16 ft., Hence, and h 28 in. × 131⁄2 = 378 in. = 31 ft. p> 256 ft.; or, p> 22 ft. To find the quantity of work required to make a double stroke of the piston, after the water reaches the level of the spout. In depressing the piston, no force is required, except that necessary to overcome the inertia of the parts and the friction. Neglecting these for the present, the quantity of work in the downward stroke, may be regarded as 0. In raising the piston, its upper surface will be pressed downwards, by the pressure of the atmosphere wh, plus the weight of the column of water from the piston to the spout; and it will be pressed upwards, by the pressure of the atmosphere, transmitted through the pump, minus the weight of a column of water, whose cross-section is equal to that of the barrel, and whose altitude is the distance from the piston to the surface of the water in the reservoir. If we subtract the latter pressure from the former, the difference will be the resultant downward pressure. This difference will be equal to the weight of a column of water, whose base is the cross-section of the barrel, and whose height is the distance of the spout above the reservoir. Denoting the height by H, the pressure will be equal to wH. The path through which the pressure is exerted during the ascent of the piston, is equal to the play of the piston, or p. Denoting the quantity of work required, by Q, we shall have, But wp is the weight of a volume of water, whose base is гор the cross-section of the barrel, and whose altitude is the play of the piston. Hence, the value of is equal to the Q quantity of work necessary to raise this volume of water from the level of the water in the reservoir to the spout. This volume is evidently equal to the volume actually delivered at each double stroke of the piston. Hence, the quantity of work expended in pumping with the sucking and lifting pump, all hurtful resistances being neglected, is equal to the quantity of work necessary to lift the amount of water, actually delivered, from the level of the water in the reservoir to the height of the spout. In addition to this work, a sufficient amount of power must be exerted, to overcome the hurtful resistances. The disadvantage of this pump, is the irregularity with which the force must act, being 0 in depressing the piston, and a maximum in raising it. This is an important objection when machinery is employed in pumping; but it may be either partially or entirely overcome, by using two pumps, so arranged, that the piston of one shall ascend as that of the other descends. Another objection to the use of this kind of pump, is the irregularity of flow, the inertia of the column of water having to be overcome at each upward stroke. This, by creating shocks, consumes a portion of the force applied. 210. Sucking and Forcing Pump. This its attached sucking-pipe B, and To explain the action of this Fig. 175. Р H pump, suppose the piston C to be depressed to its lowest limit. Now, if the piston be raised to its highest position, the air in the barrel will be rarefied, its tension will be diminished, the air in the tube B, will thrust open the valve, and a portion of it will escape into the barrel. The pressure of the external air will then force a column of water up the pipe B, until the tension of the rarefied air, plus the weight of the column of water raised, is equal to the tension of the external air. An equilibrium being produced, the valve G closes by its own weight. If, now, the piston be again depressed, the air in the barrel will be condensed, its tension will increase till it becomes greater than that of the external air, when the valve F will be thrust open, and a portion of it will escape through the delivery-pipe H. After a few double strokes of the piston, the water will rise through the valve G, and then, as the piston descends, it will be forced into the air-vessel, the air will be condensed in the upper part of the vessel, and, acting by its elastic force, will force a portion of the water up the delivery-pipe and out at the spout P. The object of the air-vessel is, to keep up a continued stream through the pipe H, otherwise it would be necessary to overcome the inertia of the entire column of water in the pipe at every double stroke. The flow having commenced, at each double stroke, a volume of water will be delivered from the spout, equal to that of a cylinder whose base is the area of the piston, and whose altitude is the play of the piston. The same relative conditions between the parts should exist as in the sucking and lifting pump. To find the quantity of work consumed at each double stroke, after the flow has become regular, hurtful resistances being neglected: When the piston is descending, it is pressed downwards by the tension of the air on its upper surface, and upwards by the tension of the atmosphere, transmitted through the delivery-pipe, plus the weight of a column of water whose base is the area of the piston, and whose altitude is the distance of the spout above the piston. This distance is variable during the stroke, but its mean value is the distance of the middle of the play below the spout. The difference between these pressures is exerted upwards, and is equal to the weight of a column of water whose base is the area of the piston, and whose altitude is the distance from the middle of the play to the spout. The distance through which the force is exerted, is equal to the play of the piston. Denoting the quantity of work during the descending stroke, by Q'; the weight of a column of water, having a base equal to the area of the piston, and a unit in altitude, by w; and the height of the spout above the middle of the the play, by h', we shall have, Q' = wh' × p. When the piston is ascending, it is pressed downwards by the tension of the atmosphere on its upper surface, and upwards by the tension of the atmosphere, transmitted through the water in the reservoir and pump, minus the weight of a column of water whose base is the area of the piston, and whose altitude is the height of the piston above the reservoir. This height is variable, but its mean value is the height of the middle of the play above the water in the reservoir. The distance through which this force is exerted, is equal to the play of the piston. Denoting the quantity of work during the ascending stroke, by Q", and the height of the middle of the play above the reservoir, by h", we have, Denoting the entire quantity of work during a double stroke, by Q, we have, But up is the weight of a volume of water, the area of whose base is that of the piston, and whose altitude is the play of the piston; that is, it is the weight of the volume delivered at the spout at each double stroke. The quantity h'+h", is the entire height of the spout above the level of the cistern. Hence, the quantity of work expended, is equal to that required to raise the entire volume delivered, from the level of the water in the reservoir to the height of the spout. To this must be added the work necessary to overcome the hurtful resistances, such as friction, &c. = If h'h', we shall have, Q'Q"; that is, the quantity of work during the ascending stroke, will be equal to that during the descending stroke. Hence, the work of the motor will be more nearly uniform, when the middle of the play of the piston is at equal distances from the reservoir and spout. Fire Engine. 211. The fire engine is essentially a double sucking and forcing pump, the two piston rods being so connected, that when one piston ascends the other descends. The sucking and delivery pipes are made of some flexible material, generally of leather, and are attached to the machine by means of metallic screw joints. The figure exhibits a cross-section of the essential part of a Fire Engine. A A' are the two barrels, C C the two pistons, connected by the rods, D D', with the lever, E E'. BE G K Fig. 176. |