9 : 4/ Mechanical and Electrical Character of the Heartbeat 167 



The subscripts refer to the right and left halves. Because the system is 

 closed, Q is the same for both. 



Equation 4 is exact and involves no approximations. It is the hydro- 

 dynamic power delivered by the heart. For humans, one may simplify 

 Equation 4 by several approximations. The velocities in the aorta and 

 pulmonary artery are about the same, whereas the aortic pressure is 

 sixfold greater. Hence, one may write 



n=$pLQ + p%Q (5) 



Because blood leaves the ventricles during only a small part of each 

 cycle (see Figure 5), the mean square velocity v 2 will be very different 

 from the square of the average velocity (v) 2 . For humans, it has been 

 found that 



y2 = 3.5(y) 2 



The average volume velocity Q must .be equal to the cross section A 

 of the aorta times the average linear velocity v, that is 



- Q 



Substituting these into Equation 5 leads to the following formula for the 

 power developed by the human heart 



n*t&« + 55f£ (6) 



It is instructive to substitute a few numbers in this formula. Some 

 typical human values are 



At rest Active Both 



p = 100 mm of Hg p = 100 mm of Hg A = 0.81 cm 2 

 Q = 3.5 1/min Q = 35 1/min /> = 1 gm/ml 



Converting to mks units and substituting in Equation 6 gives 

 At rest Active 



p L Q 1.0 w 10 w "hydrostatic" power 



1 A 



6 



3.5pQ 



3 



0.13 w 130 w — "kinetic" power 



A 2 

 n 1.1 w 140 w — total heart power 



It should be noted that for the human at rest the kinetic energy delivered 



