ASTM D5388-93(1997)
(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.
General Information
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Standards Content (Sample)
Designation: D 5388 – 93 (Reapproved 1997)
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
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 D-19 on Water
equal to unity if the cross section is not subdivided. For
D 3858 Practice for Open-Channel Flow Measurement of
subdivided sections, a is computed as follows:
Water by Velocity-Area Methods
k
i
(
3. Terminology
a
i
a5 (1)
3.1 Definitions: 3
K
T
3.1.1 For definitions of terms used in this test method, refer 2
A
T
to Terminology D 1129.
3.2 Definitions of Terms Specific to This Standard: where:
NOTE—Several of the following terms are illustrated in Fig. k and a 5 the conveyance and area of the subsection
indicated by the subscript i, and
1.
K and A 5 the conveyance and area of the total cross
3.2.1 alpha (a)—a dimensionless velocity-head coefficient
section indicated by the subscript T.
that represents the ratio of the true velocity head to the velocity
3.2.2 conveyance (K)—a measure of the carrying capacity
head computed on the basis of the mean velocity. It is assumed
of a channel without regard to slope and has dimensions of
cubic feet per second. Conveyance is computed as follows:
This test method is under the jurisdiction of ASTM Committee D-19 on Water
1.49
2/3
and is the direct responsibility of Subcommittee D19.07 on Sediments, Geomor-
K 5 AR (2)
n
phology, and Open-Channel Flow.
Current edition approved April 15, 1993. Published June 1993.
3.2.3 cross-section area (A)—the area at the water below
Barnes, H. H., Jr., “Roughness Characteristics of Natural Streams,” U.S.
the water-surface elevation that it computed. The area is
Geological Survey Water Supply Paper 1849, 1967.
Annual Book of ASTM Standards, Vol 11.01. computed as the summation of the products of mean depth
D 5388
2 2
multiplied by the width between stations of the cross section.
A 5 cross-section area, ft (m ),
3.2.4 cross sections (numbered consecutively in downstream R 5 hydraulic radius, ft, (m), and
order)—representative of a reach and channel and are posi- S 5 friction slope, ft/ft (m/m).
f
tioned as nearly as possible at right angles to the direction of 3.2.11 roughness coeffıcient (n)—or Manning’s n is used in
flow. They must be defined by coordinates of horizontal the Manning equation. Roughness coefficient or Manning’s n is
distance and ground elevation. Sufficient ground points must a measure of the resistance to flow in a channel. The factors
be obtained so that straight-line connection of the coordinates that influence the magnitude of the resistance to flow include
will adequately describe the cross-section geometry. the character of the bed material, cross-section irregularities,
depth of flow, vegetation, and channel alignment. A reasonable
3.2.5 expansion or contraction loss (ho)—in the reach is
evaluation of the resistance to flow in a channel depends on the
computed by multiplying the change in velocity head through
experience of the person selecting the coefficient and reference
the reach by a coefficient. For an expanding reach:
to texts and reports that contain values for similar stream and
ho 5 Ke~h 2 h ! (3)
v v
1 2
flow conditions (see 10.3).
and for a contracting reach:
3.2.12 velocity head (h )—in ft(m), compute velocity head
v
as follows:
ho 5 Kc~h 2 h ! (4)
v v
2 1
aV
where:
h 5 (9)
v
2g
h 5 velocity head at the respective section, and
v
Ke and Kc 5 coefficients.
where:
3.2.5.1 Discussion—The values of the coefficients can
a5 velocity-head coefficient,
V 5 the mean velocity in the cross section, ft/s (m/s), and
range from zero for ideal transitions to 1.0 for Ke and 0.5 for
g 5 the acceleration of gravity, ft/s/s (m/s/s).
Kc for abrupt changes.
3.2.6 fall (Dh)—the drop in the water surface, in ft (m),
4. Summary of Test Method
computed as the difference in the water-surface elevation at
4.1 The step-backwater test method is used to indirectly
adjacent cross sections (see Fig. 1):
determine the discharge through a reach of channel. The
Dh 5 h 2 h (5)
1 2
step-backwater test method needs only one high-water eleva-
3.2.7 friction loss (h )—the loss due to boundary friction in
f
tion and that being at the upstream most cross section. A field
the reach and is computed as follows:
survey is made to define cross sections of the stream and
determine distances between them. These data are used to
LQ
h 5 (6)
f
compute selected properties of the section. The information is
K K
1 2
used along with Manning’s n to compute the change in
where:
water-surface elevation between cross sections. For one-
L 5 length of reach, feet (metres), and
dimensional and steady flow the following equation is written
K 5 conveyance at the respective section.
for the sketch shown in Fig. 1:
3.2.8 Froude number (F)—an index to the state of flow in
h 5 h 1 h 1 hf 1 ho 2 h (10)
1 2 v v
2 1
the channel. In a prismatic channel, the flow is tranquil or
subcritical if the Froude number is less than unity and a rapid
where:
or supercritical if it is greater than unity. The Froude number is
h 5 elevation of the water surface above a common datum
computed as follows:
at the respective sections,
hf 5 the loss due to boundary friction in the reach, and
V
F 5 (7)
ho 5 the energy loss due to deceleration or acceleration of
gdm
=
the flow (in the downstream direction) in an expand-
where:
ing or contracting reach.
V 5 the mean velocity, ft/s (m/s),
dm 5 the mean depth in the cross section, feet, and 5. Significance and Use
g 5 the acceleration of gravity, ft/s/s (m/s/s).
5.1 This test method is particularly useful for determining
3.2.9 hydraulic radius (R)—defined as the area of a cross
the discharge when it cannot be measured directly (such as
section or subsection divided by the corresponding wetted
during high flow conditions) by some type of current meter to
perimeter. The wetted perimeter is the distance along the
obtain velocities and with sounding weights to determine the
ground surface of a cross section or subsection.
cross section (refer to Test Method D 3858). This test method
3.2.10 Manning’s equation—Manning’s equation for com-
requires only one high-water elevation, unlike the slope-area
puting discharge for gradually-varied flow is:
test method that requires numerous high-water marks to define
the fall in the reach. It can be used to determine a stage-
1.49
2/3 1/2
Q 5 AR S (8)
f
discharge relation without needing data from several high-
n
water events.
where:
5.1.1 The user is encouraged to verify the theoretical
3 3
Q 5 discharge, ft /s (m /s),
stage-discharge relation with direct current-meter measure-
n 5 Manning’s roughness coefficient,
ments when possible.
D 5388
5.1.2 To develop a rating curve, plot stage versus discharge instrument. The two-peg test and how to adjust the instrument
for several discharges and their computed stages on a rating are described in many surveying textbooks and in instructions
curve together with direct current-meter measurements. provided by the manufacturer. Refer to manufacturer’s manual
for the electronic instruments.
6. Interferences
9.3 If the reciprocal leveling technique is used in the survey,
6.1 The cross sections selected should be typical and rep-
it is the equivalent of the two-peg test between each of the two
resentative of the reach half way to each adjacent cross section.
successive hubs.
If there are abrupt changes between adjacent cross sections, the
9.4 Check sectional and telescoping level rods visually at
results could be suspect. The ratio of the conveyance to the
frequent intervals to be sure sections are not separated. A
conveyance at an adjacent cross section should stay within 0.7
proper fit at each joint can be quickly checked by measure-
and 1.4.
ments across the joint with a steel ta
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