PRINCIPL5S OF NAVAL ENGINEERING 



decreases (in relation to the inlet pressure). 

 However, no further increase in steam ve- 

 locity will occur when the outlet pressure 

 is reduced below 55 percent of the inlet pres- 

 sure. 



When the pressure at the outlet area of 

 a nozzle is designed to be higher than the 

 critical pressure, a simple convergent (para- 

 llel-wall) nozzle may be used. In this type of 

 nozzle, shown in figure 12-1, the cross-sectional 

 area at the outlet is the same as the cross- 

 sectional area at the throat. This type of nozzle 

 is often referred to as a nonexpanding nozzle 

 because no expansion of steam takes place 

 beyond the throat of the nozzle. 



INLET 

 REGION 



OUTLET 

 REGION 



THROAT 



147.90 

 Figure 12-1.— Simple convergent nozzle. 



When the pressure at the outlet area of a 

 nozzle is designed to be lower than the critical 

 pressure, a convergent-divergent nozzle is used 

 to control the turbulence that occurs when 

 steam expansion takes place below the critical 

 pressure ratio. In this type of nozzle, shown 

 in figure 12-2, the cross-sectional area of the 

 nozzle gradually increases from throat to out- 

 let. The critical pressure is reached in the 

 throat of the nozzle, but the gradual expansion 

 from throat to outlet allows the steam to emerge 

 finally in a steady stream or jet. Because 

 expansion takes place from the throat to the 

 outlet, this type of nozzle is often called an 

 expanding nozzle. 



The decrease in thermal energy of the 

 steam passing through a nozzle must equal 

 the increase in kinetic energy (disregarding 

 irreversible losses). The decrease in thermal 

 energy may be expressed in terms of enthalpy 

 as 



- h. 



where 

 hi 



enthalpy of the entering steam, in BTU 

 per pound 

 h2 = enthalpy of the steam leaving the nozzle, 

 in BTU per pound 



INLET 

 REGION 



THROAT 



OUTLET 

 REGION 



147.91 

 Figure 12-2.— Convergent-divergent nozzle. 



The kinetic energy of the steam jet leaving 

 the nozzle may be determined by using the 

 equation for mechanical kinetic energy: 



KE 



WV^ 

 2g 



where 



m 



KE = mechanical kinetic energy, in foot 



pounds 

 W = weight of the flowing substance, 



pounds per second 

 V = velocity, in feet per second 

 g = acceleration due to gravity (32.2 feet 



per second) 



Since we have taken the enthalpy per pound 

 of the entering and departing steam, let us as- 

 sume 1 pound of steam per second flowing from 

 the nozzle. The kinetic energy of this pound of 

 steam will then be expressed by 



KE 



A 



2g 



where V2 is the velocity, in feet per second, 

 of the steam leaving the nozzle. We may now 

 equate the expression for the decrease in thermal 

 energy and the expression for the increase in 

 kinetic energy, Thus, 



(hj - hg) (778) ft-lb 



64.4 



Since 1 BTU is equal to 778 foot-pounds, 

 we have multiplied the expression for the de- 

 crease in thermal energy by 778. This puts 

 both sides of the equation in terms of foot- 

 pounds. 



The kinetic energy of the steam leaving the 

 nozzle is directly proportional to the square of 



320 



