Page 74 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 4.5

Referring to the Figure the diameter at section 1 is d1 = 30 mm and at section 2 is d2=40

mm and the mean velocity at section 2 is v2 = 3.0 m/s. Calculate the velocity entering the
diffuser.

Solution to Example 4.5 The downstream velocity only changes

from the upstream by the ratio of the
 d  2 two areas of the pipe. As the area of
v =   2   v
1
2
 d 1  the circular pipe is a function of the
diameter, we can reduce the
 40  2 calculation further. Thus,
=
   0 . 3
 30  A  d 2 4 / d 2
v = 2 v = 2 2 v = 2 2 v
1
2
2
2
5= 3 . m s / A 1  d 1 4 / d 1
 d  2
=  2   v

2
 d 1 
Another example in the use of the continuity principle is to determine the velocities

in pipes coming from a junction. (Figure 4.5)

2

1

3

Figure 4.5

Total discharge into the junction = Total discharge out of the junction

Q1 = Q2 + Q3

A1v1 = A2v2 + A3v3

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