Equation of motion

Equation of motion

A net force fx acting on a fluid element in the direction of x is equivalent to the mass (m) of the fluid element, according to the second low of movement of newton.

                 Multiplied by the acceleration a_x in the x-    direction. Thus mathematically,

                             F_x=m x a_x  ---                    (1)

In the fluid flow, the fllowing forces are present :

(1)         F_g. gravity force.

(2)         F_p. the pressure force.

(3)         F_v. the force due to viscosity

(4)         F_t . force due to turbulenes.

(5)         F_c. Force due to compressibility.

Thus in equastion  (1).the net force.

         F_x= (f_g)_x + (f_p)_x +(f_v)_x + (f_t)_x +(f_c)_x.

(1)if the force due to compressibility, f_c is negligible the resulting net force.

              F_x= (f_g)_x + (f_p)_x +(f_v)_x + (f_t)_x

_{and equation of motion are called reynold’s equation.}