Page 154 - Water Engineering Hydraulics, Distribution and Treatment

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Chapter 5
Water Hydraulics, Transmission, and Appurtenances
EXAMPLE 5.27 VENTURI METER ANALYSIS
The deflection of the mercury in the differential gauge of a venturi meter is y = 16.5 in. (41.91 cm) shown in Fig. 5.15.
B d B
x
A
z
d A
y

L
R
Figure 5.15 Venturi meter analysis for Example 5.27.

Determine the water flow through the venturi meter if no energy is lost between A and B, and the following are known: d =
A
12 in. (30.48 cm); d = 6 in. (15.24 cm); x = 36 in. (91.44 cm); y = 16.5 in. (41.91 cm); and z = unknown.
B
Solution 1 (US Customary System):
Apply the Bernoulli equation from A to B and use A as the datum:
P v 2 P v 2 ( )
A A B B 36
+ + 0 = + + .
2g 2g 12
P A P B v 2 B v 2 A
− = − + 3.
2g 2g
From continuity equation,
Q = A v = A v .
A A B B
2 2
( ∕4)(12∕12) v = ( ∕4)(6∕12) v .
A B
4v = v .
A B
v = 0.25 v .
B
A
Apply the Bernoulli equation for L to R (s.g. mercury, Hg = 13.6):
P A 16.5 P B 36 16.5
+ z + = + + z + × 13.6.
12 12 12
P P
A B
− = 20.3 ft of water.

v 2 (0.25 v ) 2
20.3 = B − B + 3.
2g 2g
Since g = 32.2 ft/s 2
v = 34.49 ft∕s.
B
2 3
Q = A v = (6∕12) ( ∕4)(34.49) = 6.77 ft ∕s.
B B