496 



XI. HYDRODYNAMICS. 



(2 + ,) a 



which are satisfied by 



We find the buckling of the sections 

 by 129), 



Fig. 159. 



In the case of a circular beam, we have 

 D = - j and the curves of equal w are 



the contour lines of which are shown in Fig. 159. 



CHAPTER XL- 

 HYDRODYNAMICS. 



186. Equations of Motion. The equations of hydrostatics 4) 

 177 being 



i) 



where X, Y, Z are the components of the applied forces per unit 

 mass, we may obtain the equations of motion by d'Alembert's 

 Principle. 



Suppose the velocity at any point in a perfect fluid of density $ 

 is a vector q whose components u, v, w are uniform , continuous 

 differentiable functions of the point x, y, z and the time t. (The 

 notation is now changed from that of Chapter IX where u, Vj w denoted 

 displacements^) Then if we consider the motion of the fluid con- 

 tained in an element of volume dr of mass dm = $dt, we have the 

 effective forces 



