ASTM D5388-93(2007)
(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
SIGNIFICANCE AND USE
This test method is particularly useful for determining the discharge when it cannot be measured directly (such as during high flow conditions) by some type of current meter to obtain velocities and with sounding weights to determine the cross section (refer to Test Method D 3858). This test method requires only one high-water elevation, unlike the slope-area test method that requires numerous high-water marks to define the fall in the reach. It can be used to determine a stage-discharge relation without needing data from several high-water events.
5.1.1 The user is encouraged to verify the theoretical stage-discharge relation with direct current-meter measurements when possible.
5.1.2 To develop a rating curve, plot stage versus discharge for several discharges and their computed stages on a rating curve together with direct current-meter measurements.
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.
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 appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:D5388 −93(Reapproved 2007)
Standard Test Method for
Indirect Measurements of Discharge by Step-Backwater
Method
This standard is issued under the fixed designation D5388; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.1 For definitions of terms used in this test method, refer
to Terminology D1129.
1.1 This test method covers the computation of discharge of
3.2 Definitions of Terms Specific to This Standard:
water in open channels or streams using representative cross-
NOTE—Several of the following terms are illustrated in Fig.
sectional characteristics, the water-surface elevation of the
1.
upstream-most cross section, and coefficients of channel
3.2.1 alpha (α)—a dimensionless velocity-head coefficient
roughness as input to gradually-varied flow computations.
that represents the ratio of the true velocity head to the velocity
1.2 This test method produces an indirect measurement of
head computed on the basis of the mean velocity. It is assumed
the discharge for one flow event, usually a specific flood. The
equal to unity if the cross section is not subdivided. For
computed discharge may be used to define a point on the
subdivided sections, α is computed as follows:
stage-discharge relation.
k
i
1.3 The values stated in inch-pound units are to be regarded
(
a
i
as the standard. The SI units given in parentheses are for α 5 (1)
K
T
information only.
A
T
1.4 This standard does not purport to address all of the
where:
safety concerns, if any, associated with its use. It is the
k and a = the conveyance and area of the subsection indi-
responsibility of the user of this standard to establish appro-
cated by the subscript i , and
priate safety and health practices and determine the applica-
K and A = the conveyance and area of the total cross
bility of regulatory limitations prior to use.
section indicated by the subscript T.
2. Referenced Documents
3.2.2 conveyance(K)—ameasureofthecarryingcapacityof
2.1 ASTM Standards:
a channel without regard to slope and has dimensions of cubic
D1129 Terminology Relating to Water
feet per second. Conveyance is computed as follows:
D2777 Practice for Determination of Precision and Bias of
1.49
2/3
Applicable Test Methods of Committee D19 on Water
K 5 AR (2)
n
D3858 Test Method for Open-Channel Flow Measurement
3.2.3 cross-section area (A)—theareaatthewaterbelowthe
of Water by Velocity-Area Method
water-surface elevation that it computed. The area is computed
3. Terminology
as the summation of the products of mean depth multiplied by
3.1 Definitions: the width between stations of the cross section.
3.2.4 cross sections (numbered consecutively in downstream
This test method is under the jurisdiction of ASTM Committee D19 on Water
order)—representative of a reach and channel and are posi-
and is the direct responsibility of Subcommittee D19.07 on Sediments,
tioned as nearly as possible at right angles to the direction of
Geomorphology, and Open-Channel Flow.
flow. They must be defined by coordinates of horizontal
Current edition approved June 15, 2007. Published July 2007. Originally
approved in 1993. Last previous edition approved in 2002 as D5388 – 93 (2002).
distance and ground elevation. Sufficient ground points must
DOI: 10.1520/D5388-93R07.
be obtained so that straight-line connection of the coordinates
Barnes, H. H., Jr., “Roughness Characteristics of Natural Streams,” U.S.
will adequately describe the cross-section geometry.
Geological Survey Water Supply Paper 1849, 1967.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.2.5 expansion or contraction loss (ho)—in the reach is
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
computed by multiplying the change in velocity head through
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. the reach by a coefficient. For an expanding reach:
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5388−93 (2007)
V
F 5 (7)
=gdm
where:
V = the mean velocity, ft/s (m/s),
dm = the mean depth in the cross section, feet, and
g = the acceleration of gravity, ft/s/s (m/s/s).
3.2.9 hydraulic radius (R)—defined as the area of a cross
section or subsection divided by the corresponding wetted
perimeter. The wetted perimeter is the distance along the
ground surface of a cross section or subsection.
3.2.10 Manning’s equation—Manning’s equation for com-
puting discharge for gradually-varied flow is:
1.49
2/3 1/2
Q 5 AR S (8)
f
n
where:
3 3
Q = discharge, ft /s (m /s),
n = Manning’s roughness coefficient,
2 2
A = cross-section area, ft (m ),
FIG. 1 Definition Sketch of Step-Backwater Reach
R = hydraulic radius, ft, (m), and
S = friction slope, ft/ft (m/m).
f
3.2.11 roughness coeffıcient (n)—or Manning’s n is used in
theManningequation.RoughnesscoefficientorManning’snis
ho 5 Ke h 2 h (3)
~ !
v v
1 2
a measure of the resistance to flow in a channel. The factors
that influence the magnitude of the resistance to flow include
and for a contracting reach: the character of the bed material, cross-section irregularities,
depth of flow, vegetation, and channel alignment.Areasonable
ho 5 Kc h 2 h (4)
~ !
v v
2 1
evaluation of the resistance to flow in a channel depends on the
experience of the person selecting the coefficient and reference
where:
to texts and reports that contain values for similar stream and
h = velocity head at the respective section, and
flow conditions (see 10.3).
v
Ke and Kc = coefficients.
3.2.12 velocity head (h )—in ft(m), compute velocity head
v
as follows:
3.2.5.1 Discussion—Thevaluesofthecoefficientscanrange
from zero for ideal transitions to 1.0 for Ke and 0.5 for Kc for
αV
h 5 (9)
v
abrupt changes.
2g
3.2.6 fall (∆h)—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):
α = velocity-head coefficient,
V = the mean velocity in the cross section, ft/s (m/s), and
∆h 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
the reach and is computed as follows:
4. Summary of Test Method
LQ
h 5 (6)
f
4.1 The step-backwater test method is used to indirectly
K K
1 2
determine the discharge through a reach of channel. The
step-backwater test method needs only one high-water eleva-
where:
tion and that being at the upstream most cross section. A field
L = length of reach, feet (metres), and
survey is made to define cross sections of the stream and
K = conveyance at the respective section.
determine distances between them. These data are used to
3.2.8 Froude number (F)—an index to the state of flow in compute selected properties of the section. The information is
the channel. In a prismatic channel, the flow is tranquil or used along with Manning’s n to compute the change in
subcritical if the Froude number is less than unity and a rapid water-surface elevation between cross sections. For one-
or supercritical if it is greater than unity.The Froude number is dimensional and steady flow the following equation is written
computed as follows: for the sketch shown in Fig. 1:
D5388−93 (2007)
h 5 h 1h 1hf1ho 2 h (10) 7. Apparatus
1 2 v v
2 1
7.1 The equipment generally used for a “transit-stadia”
survey is recommended. An engineer’s transit, a self-leveling
where:
level with azimuth circle, newer equipment using electronic
h = elevationofthewatersurfaceaboveacommondatum
circuitry, or other advanced surveying instruments may be
at the respective sections,
used. Standard level rods, a telescoping 25-ft (7.62-m) level
hf = the loss due to boundary friction in the reach, and
rod, rod levels, head levels, steel and metallic tapes, tag lines
ho = the energy loss due to deceleration or acceleration of
(small wires with markers fixed at known spacings), vividly
the flow (in the downstream direction) in an expand-
colored flagging, survey stakes, a camera (preferably stereo)
ing or contracting reach.
with built-in light meter with color film, and ample note paper
are necessary items.
5. Significance and Use
7.2 Additional equipment that may expedite a survey in-
5.1 This test method is particularly useful for determining
cludes axes, machetes, a boat with oars and motor, hip boots,
the discharge when it cannot be measured directly (such as
waders, rain gear, sounding equipment, and two-way radios.
during high flow conditions) by some type of current meter to
7.3 Safety equipment should include life jackets, first aid
obtain velocities and with sounding weights to determine the
kit, drinking water, and pocket knives.
cross section (refer to Test Method D3858). This test method
requires only one high-water elevation, unlike the slope-area
8. Sampling
test method that requires numerous high-water marks to define
the fall in the reach. It can be used to determine a stage-
8.1 Sampling as defined in Terminology D1129 is not
discharge relation without needing data from several high-
applicable in this test method.
water events.
5.1.1 The user is encouraged to verify the theoretical 9. Calibration
stage-discharge relation with direct current-meter measure-
9.1 Check the surveying instruments, levels, transits, etc.
ments when possible.
adjustments before each use, and possibly daily when in
5.1.2 To deve
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