ASTM D5388-93(2002)
(Test Method)Standard Test Method for Indirect Measurements of Discharge by Step-Backwater Method
Standard Test Method for Indirect Measurements of Discharge by Step-Backwater Method
SCOPE
1.1 This test method covers the computation of discharge of water in open channels or streams using representative cross-sectional characteristics, the water-surface elevation of the upstream-most cross section, and coefficients of channel roughness as input to gradually-varied flow computations.
1.2 This test method produces an indirect measurement of the discharge for one flow event, usually a specific flood. The computed discharge may be used to define a point on the stage-discharge relation.
1.3 The values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are for information only.
1.4 This standard does not purport to address all of the safety problems, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: D 5388 – 93 (Reapproved 2002)
Standard Test Method for
Indirect Measurements of Discharge by Step-Backwater
Method
This standard is issued under the fixed designation D 5388; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This test method covers the computation of discharge of
water in open channels or streams using representative cross-
sectional characteristics, the water-surface elevation of the
upstream-most cross section, and coefficients of channel
roughness as input to gradually-varied flow computations.
1.2 This test method produces an indirect measurement of
the discharge for one flow event, usually a specific flood. The
computed discharge may be used to define a point on the
stage-discharge relation.
1.3 The values stated in inch-pound units are to be regarded
as the standard. The SI units given in parentheses are for
information only.
1.4 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
D 1129 Terminology Relating to Water
FIG. 1 Definition Sketch of Step-Backwater Reach
D 2777 Practice for Determination of Precision and Bias of
Applicable Methods of Committee D19 on Water
3.2.1 alpha (a)—a dimensionless velocity-head coefficient
D 3858 Practice for Open-Channel Flow Measurement of
that represents the ratio of the true velocity head to the velocity
Water by Velocity-Area Methods
head computed on the basis of the mean velocity. It is assumed
equal to unity if the cross section is not subdivided. For
3. Terminology
subdivided sections, a is computed as follows:
3.1 Definitions:
k
3.1.1 For definitions of terms used in this test method, refer i
(
to Terminology D 1129. a
i
a5 (1)
3.2 Definitions of Terms Specific to This Standard:
K
T
A
T
NOTE—Several of the following terms are illustrated in Fig.
1.
where:
k and a = the conveyance and area of the subsection
1 indicated by the subscript i, and
This test method is under the jurisdiction of ASTM Committee D19 on Water
K and A = the conveyance and area of the total cross
and is the direct responsibility of Subcommittee D19.07 on Sediments, Geomor-
phology, and Open-Channel Flow.
section indicated by the subscript T.
Current edition approved April 15, 1993. Published June 1993.
3.2.2 conveyance (K)—a measure of the carrying capacity
Barnes, H. H., Jr., “Roughness Characteristics of Natural Streams,” U.S.
of a channel without regard to slope and has dimensions of
Geological Survey Water Supply Paper 1849, 1967.
Annual Book of ASTM Standards, Vol 11.01. cubic feet per second. Conveyance is computed as follows:
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5388 – 93 (2002)
1.49
perimeter. The wetted perimeter is the distance along the
2/3
K 5 AR (2)
n
ground surface of a cross section or subsection.
3.2.10 Manning’s equation—Manning’s equation for com-
3.2.3 cross-section area (A)—the area at the water below
puting discharge for gradually-varied flow is:
the water-surface elevation that it computed. The area is
1.49
2/3 1/2
computed as the summation of the products of mean depth
Q 5 AR S (8)
f
n
multiplied by the width between stations of the cross section.
3.2.4 cross sections (numbered consecutively in downstream
order)—representative of a reach and channel and are posi- where:
3 3
tioned as nearly as possible at right angles to the direction of Q = discharge, ft /s (m /s),
n = Manning’s roughness coefficient,
flow. They must be defined by coordinates of horizontal
2 2
A = cross-section area, ft (m ),
distance and ground elevation. Sufficient ground points must
R = hydraulic radius, ft, (m), and
be obtained so that straight-line connection of the coordinates
S = friction slope, ft/ft (m/m).
f
will adequately describe the cross-section geometry.
3.2.11 roughness coeffıcient (n)—or Manning’s n is used in
3.2.5 expansion or contraction loss (ho)—in the reach is
theManningequation.RoughnesscoefficientorManning’s nis
computed by multiplying the change in velocity head through
the reach by a coefficient. For an expanding reach: a measure of the resistance to flow in a channel. The factors
that influence the magnitude of the resistance to flow include
ho 5 Ke~h 2 h ! (3)
v v
1 2
the character of the bed material, cross-section irregularities,
depth of flow, vegetation, and channel alignment.Areasonable
and for a contracting reach:
evaluation of the resistance to flow in a channel depends on the
ho 5 Kc~h 2 h ! (4)
v v
2 1 experience of the person selecting the coefficient and reference
to texts and reports that contain values for similar stream and
flow conditions (see 10.3).
where:
h = velocity head at the respective section, and
3.2.12 velocity head (h )—in ft(m), compute velocity head
v
v
Ke and Kc = coefficients.
as follows:
3.2.5.1 Discussion—The values of the coefficients can
aV
range from zero for ideal transitions to 1.0 for Ke and 0.5 for
h 5 (9)
v
2g
Kc for abrupt changes.
3.2.6 fall (Dh)—the drop in the water surface, in ft (m),
computed as the difference in the water-surface elevation at
where:
adjacent cross sections (see Fig. 1): a = velocity-head coefficient,
V = the mean velocity in the cross section, ft/s (m/s), and
Dh 5 h 2 h (5)
1 2
g = the acceleration of gravity, ft/s/s (m/s/s).
3.2.7 friction loss (h )—the loss due to boundary friction in
f
4. Summary of Test Method
the reach and is computed as follows:
4.1 The step-backwater test method is used to indirectly
LQ
h 5 (6) determine the discharge through a reach of channel. The
f
K K
1 2
step-backwater test method needs only one high-water eleva-
tion and that being at the upstream most cross section. A field
where:
survey is made to define cross sections of the stream and
L = length of reach, feet (metres), and
determine distances between them. These data are used to
K = conveyance at the respective section.
compute selected properties of the section. The information is
3.2.8 Froude number (F)—an index to the state of flow in
used along with Manning’s n to compute the change in
the channel. In a prismatic channel, the flow is tranquil or
water-surface elevation between cross sections. For one-
subcritical if the Froude number is less than unity and a rapid
dimensional and steady flow the following equation is written
or supercritical if it is greater than unity.The Froude number is
for the sketch shown in Fig. 1:
computed as follows:
h 5 h 1 h 1 hf 1 ho 2 h (10)
1 2 v v
2 1
V
F 5 (7)
gdm
=
where:
h = elevation of the water surface above a common datum
where:
at the respective sections,
V = the mean velocity, ft/s (m/s),
hf = the loss due to boundary friction in the reach, and
dm = the mean depth in the cross section, feet, and
ho = the energy loss due to deceleration or acceleration of
g = the acceleration of gravity, ft/s/s (m/s/s).
the flow (in the downstream direction) in an expand-
3.2.9 hydraulic radius (R)—defined as the area of a cross
ing or contracting reach.
section or subsection divided by the corresponding wetted
D 5388 – 93 (2002)
5. Significance and Use 7.2 Additional equipment that may expedite a survey in-
cludes axes, machetes, a boat with oars and motor, hip boots,
5.1 This test method is particularly useful for determining
waders, rain gear, sounding equipment, and two-way radios.
the discharge when it cannot be measured directly (such as
7.3 Safety equipment should include life jackets, first aid
during high flow conditions) by some type of current meter to
kit, drinking water, and pocket knives.
obtain velocities and with sounding weights to determine the
cross section (refer to Test Method D 3858). This test method
8. Sampling
requires only one high-water elevation, unlike the slope-area
8.1 Sampling as defined in Terminology D 1129 is not
test method that requires numerous high-water marks to define
applicable in this test method.
the fall in the reach. It can be used to determine a stage-
discharge relation without needing data from several high-
9. Calibration
water events.
9.1 Check the surveying instruments, levels, transits, etc.
5.1.1 The user is encouraged to verify the theoretical
adjustments before each use, and possibly daily when in
stage-discharge relation with direct current-meter measure-
continuous use, or after some occurrence that may have
ments when possible.
affected the adjustment.
5.1.2 To develop a rating curve, plot stage versus discharge
9.2 The standard check is the two-peg or double-peg test. If
for several discharges and their computed stages on a rating
the error is over 0.03 ft in 100 ft (0.009 m in 30.4 m), adjust
curve together with direct current-meter measurements.
instrument. The two-peg test and how to adjust the instrument
are described in many surveying textbooks and in instructions
6. Interferences
provided by the manufacturer. Refer to manufacturer’s manual
for the electronic instruments.
6.1 The cross sections selected sho
...
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