Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 11–15. The pressure field is given by
where P0 is the pressure at x =0. Generate an expression for the rate of change of pressure following a fluid particle.
PROBLEM: Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P11–15). A simple approximate velocity field for this flow is
where U0 is the horizontal speed at x= 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components ax and ay and (2) as acceleration vector .
Consider a duct flow which is steady, converging and incompressible. The flow happens at two dimensional space.
The pressure field is given by
P = - ----(1)
Where P0 is the pressure at x = 0
To generate an expression for the rate of change of pressure following a fluid particle
The material derivative of pressure function as given in the velocity field
= + + + -------(2)
In the case of steady flow = 0
And two dimensional flow = 0
The (2) becomes
= + -----------------------(3)
Differentiating (1) with respect to x