are not additive. Out of all the cases that can be constructed in this manner, only the most 

 interesting will be mentioned. 



The section on units in Chapter I, Section 18, may be noted. 



The older convention as to the signs of and xh described in Sections 6, 13, and 16, 

 may also be noted; it is often encountered in the literature. Formulas based on this older 

 convention may be obtained by changing the sign before every symbol representing a velocity 

 component. 



35. UNIFORM MOTION 



SOME SIMPLE TYPES OF FLOW 



w - Az + C, A = a + ib 



where a and b are real constants and C is another constant, real or complex. This transforma- 

 tion was discussed mathematically in Section 24. Since w = ci> + i i/t, 



cfi = ax - by, it/ = bx + ay 



I ^^ I 

 u=-a, V = b, g = — - = Ul = (a2 + 62y/2 



I (22 I 



The flow is thus one of uniform translation. The flow net, illustrated in Figure 40, consists 

 of straight lines. 



If the fluid is moving at velocity (7 in a direction inclined at an angle a to the negative 

 ir-axis, as in Figure 41, A = U,u = -a = -U cosot , v = b = - U sin a , and, with omission of 

 the physically meaningless constant C, 



w = U (coso - i sina ) 2 = U ze '" 

 (For notation and method; see Section 34; tleference 2, Section 6.0.) 



[35a] 



Figure 40 — Flow net for uniform flow. 



74 



