For the velocity field of Prob. 11–2, calculate the fluid acceleration along the nozzle centerline as a function of x and the given parameters.

PROBLEM: Consider the steady flow of water through an axisymmetric garden hose nozzle (see figure). Along the centerline of the nozzle, the water speed increases from uentrance to uexit as sketched. Measurements reveal that the centerline water speed increases parabolically through the nozzle. Write an equation for centerline speed u(x), based on the parameter given here, from x=0 to x=L.

Solution to 21P

Step 1</p>

We need to find the acceleration along x axis. We are given that the fluid flow is decreasing parabolically while flowing through the diffuser.

Thus we will consider the material acceleration. The flow is steady and there are no components of velocity in other directions except x axis.

Velocity of the centreline velocity is given by,

Step 2</p>

From the equation of acceleration for x axis,

Thus,