Figure 101 — Pressure in the symmetrical 



flow past a circular cylinder, along the 



axis of the flow, over the cylinder, 



and in the equatorial plane. 



See Equations L67m,n,o]. 



At points inside the cylindrical surface, the formulas may be used to represent the 

 flow caused inside of a rigid cylindrical shell of radius a by a line dipole of moment n = a^V 

 on its axis. In this use of the formulas, U represents merely a constant having the value 



Changing the sign of U reverses all velocities, without affecting the flow net or the 

 pressure. 



(For notation and method, see Section 34; Reference 1, Article 68; Reference 2, 

 Section 6.22, 6.23.) 



68. TRANSLATION OF A CIRCULAR CYLINDER 



By changing to a frame of reference that is moving toward negative x at velocity U, a 

 description is obtained of a circular cylinder that is moving toward positive x at velocity U 

 while the fluid is at rest at infinity. The change adds to ic a term -Uz, representing uniform 

 flow of the fluid toward positive x, so that, from [67a], 



a^V cos d ,,, sin 

 w = • , <f) = a-^U =-^ — , xjj = -a^U . 



[68a,b,c] 



These formulas represent the dipole transformation, as discussed in Section 37. The axes of 

 coordinates move here with the cylinder. The streamlines are arcs of circles, as illustrated 

 in Figure 102. 



The velocity components and the value of q^ are: 



u= a^U 



v = a^V 



2xy 



[68d,e] 



,,, cos 6 „,, sin 6 , a^V^ 



q=a^U , qa = a^U ; 9^= . 



,2 '' ,2 ,4 



[68f,g,h] 



151 



