Water flows vertically upward in a circular cross-sectional pipe. A device is installed between cross-

sections (1) and (2) that alters flow velocity distribution. At section (1), the velocity Vin is uniform.

At section (2), the velocity profile is Ve(1-r/R), where Ve is the centerline velocity, r is the radial

coordinate, and R is the pipe radius. The pressures at the cross sections are p₁ and p2, respectively,

and p₁=p2. The distance between the cross sections is h. The head loss due to minor losses is

given by IL,minor = KL g

1.

2.

3.

Hint:

Find the centerline flow velocity at section (2).

Find the kinetic energy coefficient a2 at section (2).

Develop an expression for the minor loss coefficient K₁ between sections (1) and (2).

j(1-2)'rd

where a is a constant.

0

R

h!

20

19

(2)

(1)

Figure 4: Sketch for Problem 4.