Module 5: Reynolds Transport Theorem
  Lecture 15: Equation of motion
 
 
Equation of motion

(Differential form of momentum conservation rate).
Before we apply Reynolds Transport theorem, it is important to understand the forces acting on a fluid-element.
We have earlier noted that the only force acting on a static fluid is the normal force or the pressure acting normal to the surface of the fluid element.

Static fluid: 

 
(Fig. 15a)
In flowing fluid, there is a tangential force or shear force acting parallel to the surface of the fluid-element. Thus, there are two types of stress developed in a flowing fluid: one is the normal stress,  and the other is the shear stress,  :
 
(Fig. 15b)