B • TURBULENT FLOW 



convey an idea of the order of magnitude of the ratio of turbulent vis- 

 cosity to ordinary viscosity. 



When the spreading is linear, as it is for jets, the angle of spreading 

 affords a convenient means of visualizing the size. This angle may be 

 found from Eq. 30-5 and 30-8 in terms of some suitably defined width. 

 If we take this to be the line along which U /U^ = -|, we find that the 

 plane jet is a wedge with a half angle of approximately 6|- degrees and 

 the round jet is a cone with a half angle of approximately 5 degrees. 

 These angles are independent of the strength of the jet. The spreading 

 of laminar jets, on the other hand, depends on the strength, becoming 

 narrower as the strength increases. The plane laminar jet is not wedge- 

 shaped; the width increases with xi These differences between turbulent 

 flow and laminar flow are mentioned as additional illustrations of the 

 effect of an eddy viscosity which is regulated by the flow itself. 



B,31. Eifect of Density Differences and Compressibility on Jets 

 with Surrounding Air Stationary. In jet propulsion the jet is much 

 hotter than the surrounding air and it issues at a high relative velocity. 

 Density differences and compressibility are therefore expected to be of 

 some importance. When we examine the situation realistically, however, 

 we find that both temperature difference and relative velocity diminish 

 rapidly with distance, and the jet soon behaves much like the constant- 

 density, incompressible jet previously treated. When the jet issues rear- 

 ward from a moving vehicle, it does not emerge into a surrounding me- 

 dium at rest but rather into a medium with an axial velocity in the same 

 direction. Under this condition the jet spreads more slowly, and the tem- 

 perature and relative velocity diminish more slowly with distance from 

 the orifice. The extent over which density and compressibility effects are 

 possibly important therefore depends on the velocity of the outer stream. 

 The effect of an outer velocity will be considered in Art. 32; here the 

 problem is considered for the surrounding medium stationary with respect 

 to the nozzle. 



The work of Corrsin and Uberoi on the heated round jet [123] has 

 contributed substantially to what is known about the hot jet issuing into 

 still surrounding air. They studied the jet issuing from a 1-inch orifice 

 with velocities ranging from 65 to 115 ft/sec. The initial temperature rise 

 was made slight when it was desired to study the spread of momentum 

 and heat without introducing significant effects of density difference, and 

 was raised to about 300°C when the effect of density was to be studied. 

 In the latter case the density ratio was pi/po = 2, where po is the density 

 of the jet at the nozzle and pi is the density of the surrounding air. 



The principal effects are illustrated in Fig. B,31a and B,31b taken 

 from the report of Corrsin and Uberoi. Fig. B,31a shows the velocity and 

 temperature profiles 16 nozzle diameters downstream. From these it is 



( 176 > 



