WORK DONE BY A PUMP 367 



it is necessary to replace the rigid conduit by an elastic tube. 

 Such a tube would, of course, if rigid, permit a certain flow of 

 fluid per unit of time per unit of pressure, say with a constant 

 velocity of (v). Now on the descent of the piston more water 

 tends to be forced into the conduit than can be passed out with 

 this velocity (v). The elastic walls distend till their ekistic power 

 exactly counterbalances the extra energy, and the fluid has an 

 outflow velocity of (v). The inflvix of water having ceased, the 

 steady pressure of the distended walls of the tube as they recoil 

 keeps the fluid at the constant velocity (v). In this way the 

 fluid is held under a continuous pressure, and, provided the pump 

 has the proper frequency, the outflow remains practically constant. 

 That is, the elastic tube really converts an interjnittent inflow into 

 a constant outflow, the property of elasticity preserving 7iormal 

 conditions of flow even during periods when the piston is not 

 descending. 



The value of the work done by a pump may be calculated 

 approximately by the formula 



W=QR + — + 0, 



where W (gram-metres), is the work done at each stroke, m is the 

 mass in grams and Q the stroke volume, the quantity of fluid in 

 c.c. expelled at each stroke ; R is the average resistance of the 

 circuit, V (metres per sec.) is the velocity of expulsion, and g is the 

 acceleration due to gravity = 9.8 metres per sec. per sec. That is, 



niv^ 

 QR represents the resistance pressure (r in Fig. 87) and (v in 



"a 

 Fig. 87) the velocity pressure, while O is the energy expended in 

 overcoming the resistance to outflow at the orifice of the pump. 



Such a system of single stroke pump and elastic regiflator does 

 not differ in essentials from the one contrived by nature to provide 

 a perfect transport service to every unit of a complex organism 

 like the human body. In Fig. 88 a simple force pump and its 

 circulating system is compared with the left ventricle, aorta, etc. 



The manner in which the contents are forced out from the 

 ventricle differs in some details from that obtaining in the water 

 pump. In the latter, a rigid piston descends within a rigid 

 cylinder and thus obliterates the space of the main chamber and 

 forces the water through the outflow pi])e. The ])ower necessary 

 to drive the phuiger home is derived from an engine of some sort, 

 external to and independent of the pump itself. In the heart, 

 the elastic muscular walls of the ventricles contract as a whole, 



