Page 122 - Fluid mechanics, heat transfer, and mass transfer

FLOW MEASUREMENT 99

& With sharp-edged weir, the sheet of discharging
liquid, contracts as it leaves the opening and free
discharge occurs.
& Rounding upstream edge will reduce the contraction
and increase the flow rate for a given head.
& That is, for a given flow rate, head will be less than
that for sharp-edged weir.
FIGURE 4.40 Rectangular and triangular types of weirs.
& Result is that accuracy of head readings will decrease
for a blunt-edged weirs.
level (head) behind the barrier. The head is a function
of flow velocity, and, therefore, the flow rate through . Give the equations for flow measurement in open
the device. channels using rectangular and V-notches.
& Weirs consist of vertical plates with sharp crests. The & Flow over wide rectangular weirs:
top of the plate can be straight or notched. Weirs are
classified in accordance with the shape of the notch. q weir ¼ C d bg 1=2 H 3=2 : ð4:12Þ
The basic types are rectangular, V-notch, and
trapezoidal. where q weir is the volumetric flow rate measured in
3
m /s and C d is the dimensionless weir coefficient. For
& The two types of weirs commonly used are the
turbulent upstream flow, C d depends on weir geom-
rectangular weir and the triangular weir as shown
etry, b is the width of the weir in meters. For narrow
in Figure 4.40.
weirs with side walls, b is to be replaced by b 0.1H,
& The liquid flows over the weir, and the height, h 0
where H is the height of the weir in meters, and
(weir head), in m is measured above the flat base or
g ¼ 9.81.
the notch as shown. This head should be measured at
& C d can be computed from the following empirical
a distance of about 3h 0 m upstream of the weir by a
equations:
level or float gauge.
& Weirs are used for open channel flow measurement,
For sharp-crested weirs;
as liquids flow in open channels in process plants,
rivers, canals, drains, and so on. An example in
C d 0:564þ0:0846L=H; for L=H < 0:07:
process equipment is in plate distillation columns.
3 ð4:13Þ
& The equation for thevolumetric flow rate q in m /s for
a rectangular weir is given by
Forbroad-crestedweirs;
0:5
1:5
q ¼ 0:415ðL 0:2h 0 Þh ð2gÞ : ð4:10Þ
0 C d 0:462 for 0:08 < H=L < 0:33: ð4:14Þ
For a triangular notch, where L is the length of theweir in meters and H is the
height of the weir in meters.
0:5
2:5
q ¼½0:31h Šð2gÞ =tan u; ð4:11Þ
0
& Flow over triangular notches with the angle, 2u,
3
where q is measured in m /s; L is the crest length in 1=2 5:2
2
meters; g ¼ 9.80665 m/s ; h 0 ¼ weir height in meters; Q 0:44 tan u g H ; for 10 < u 50
and Ø is the angle as shown in Figure 4.40. These ð4:15Þ
formulas were developed for flow of water and
require corrections for other liquids. & The V-notch is more sensitive at low flow rates (large
. What is the difference between a sharp-edged weir and a H for a small Q) and thus is popular in laboratory
rounded upstream-edged weir? measurements of channel flow rates.