KgUATiONs OF Motion of a \ iscou.s LigLiu. 



-6\f 



Derivatigx of Equations. 



Section I. — Equations of motion of a perfect fluid. 



D'Alembert's Principle: Since D'Alembert's Principle is 

 used so frequently in what follows, it may be well to say by 

 way of explanation of this principle that its use means the 

 equatinj^ of 



Impressed Force — Pressure — Expressed Force 

 to the forces lost through friction. 



An Ideal Fluid. — With this as with other problems, it 

 is easier to consider first the ideal condition. An ideal fluid 

 is one in which there is no friction; the particles move by 

 one another without causing any mutual retardation; hence 

 without any loss of energy. 



The Derivation of the Equations of Motion of a Perfect 

 Fluid. — To derive the equations of motion of a perfect fluid 

 is a comparatively easy matter. 



Y CD 



(XYZ) 



FIG. 2 



Let ^4 D (Fig 1) represent an element of such fluid; x, y, z 

 be the coordinates of the point J.y A G, A B, and .4 H equal 

 to dx, dy, and dz respectively; X, Y, and Z the impressed 

 forces in directions x, y, and z; and «, v, and w the velocities 



