42 



Colorado College Studies. 



Similarily the increments in the directions of the y and z 

 axes are found to be 



d{vp) 



and 



dy 

 d ( ivp ) 

 dz 



dt dx dy dz 

 dt dx dy dz. 



Equatinii: the whole increment to the partial increments and 

 dividing by dt dx dy dz, we obtain 



dp_d{up) d(vp) d(ivp) 

 dt dx dy dz 



But for an incompressible fluid, ," being constant, this 

 becomes 



dn dv div _^ 



dx dy dz 



Section II. — The Equations of Motion of a Viscous Fluid. 



Having determined the equations of motion of a perfect 

 fluid when referred to rectangular coordinates, we will now 

 consider a viscous fluid. This consideration will combine 

 those forces already dealt with in the case of a perfect fluid 

 and the forces lost through internal friction. 



The problem is to determine the relations existing between 

 these lost forces and the velocities. 



Coefficient of Viscosity. — It is necessary at this point to 

 define a quantity called the coefficient of viscosity. 



E M jj p 



FIG. 4. 



li AE D R represents the initial position of an element 



