ASTM D5388-21

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Designation: D5388 − 93 (Reapproved 2013) D5388 − 21
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
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 values given in parentheses are for
information only.mathematical conversions to SI units that are provided for information only and are not considered standard.
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 appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D1129 Terminology Relating to Water
D2777 Practice for Determination of Precision and Bias of Applicable Test Methods of Committee D19 on Water
D3858 Test Method for Open-Channel Flow Measurement of Water by Velocity-Area Method
3. Terminology
3.1 Definitions:
3.1.1 For definitions of terms used in this test method, standard, refer to Terminology D1129.
3.2 Definitions of Terms Specific to This Standard:
This test method is under the jurisdiction of ASTM Committee D19 on Water and is the direct responsibility of Subcommittee D19.07 on Sediments, Geomorphology,
and Open-Channel Flow.
Current edition approved Jan. 1, 2013Nov. 1, 2021. Published January 2013January 2022. Originally approved in 1993. Last previous edition approved in 20072013 as
D5388 – 93 (2007).(2013). DOI: 10.1520/D5388-93R13.10.1520/D5388-21.
Barnes, H. H., Jr., “Roughness Characteristics of Natural Streams,” U.S. Geological Survey Water Supply Paper 1849, 1967.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5388 − 21
NOTE—Several of the following terms are illustrated in Fig. 1.
3.2.1 alpha (α)—(α), n—a dimensionless velocity-head coefficient that represents the ratio of the true velocity head to the velocity
head computed on the basis of the mean velocity. It is assumed equal to unity if the cross section is not subdivided. For subdivided
sections, α is computed as follows:
k
i
(
a
i
α5 (1)
K
T
A
T
where:
k and a = the conveyance and area of the subsection indicated by the subscript I, and
K and A = the conveyance and area of the total cross section indicated by the subscript T.
3.2.2 conveyance (K)—(K), n—a measure of the carrying capacity of a channel without regard to slope and has dimensions of
cubic feet per second. Conveyance is computed as follows:
1.49
2/3
K 5 AR (2)
n
3.2.3 cross-section area (A)—(A), n—the area at the water below the water-surface elevation that it computed. The area is
computed as the summation of the products of mean depth multiplied by the width between stations of the cross section.
3.2.4 cross sections (numbered consecutively in downstream order)—order), n—representative portions of a reach and channel and
are positioned as nearly as possible at right angles to the direction of flow. They must be defined by coordinates of horizontal
distance and ground elevation. Sufficient ground points must be obtained so that straight-line connection of the coordinates will
adequately describe the cross-section geometry.
3.2.5 expansion or contraction loss (ho)—(ho), n—in the reach a value is computed by multiplying the change in velocity head
through the reach by a coefficient. For an expanding reach:
ho 5 Ke h 2 h (3)
~ !
v v
1 2
and for a contracting reach:
FIG. 1 Definition Sketch of Step-Backwater Reach
D5388 − 21
ho 5 Kc h 2 h (4)
~ v v !
2 1
where:
h = velocity head at the respective section, and
v
Ke and Kc = coefficients.
3.2.5.1 Discussion—
The values of the coefficients can range from zero for ideal transitions to 1.0 for Ke and 0.5 for Kc for abrupt changes.
3.2.6 fall (Δh)—(Δh), n—the drop in the water surface, in ft (m), computed as the difference in the water-surface elevation at
adjacent cross sections (see Fig. 1):
Δh 5 h 2 h (5)
1 2
3.2.7 friction loss (h )—), n—the loss due to boundary friction in the reach and is computed as follows:
f
L Q
h 5 (6)
f
K K
1 2
where:
L = length of reach, feet (metres), and
K = conveyance at the respective section.
3.2.8 Froude number (F)—(F), n—an index to the state of flow in the channel. In a prismatic channel, the flow is tranquil or
subcritical if the Froude number is less than unity and a rapid or supercritical if it is greater than unity. The Froude number is
computed as follows:
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)—(R), n—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—equation, n—Manning’sthe equation for computing discharge for gradually-varied flow is:
1.49
2/3 1/2
Q 5 A R 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 ),
R = hydraulic radius, ft, (m), and
S = friction slope, ft/ft (m/m).
f
3.2.11 roughness coeffıcient (n)—(n) (or Manning’s n is used in the Manning equation) (n), n—or Manning’s n is used in the
Manning equation. Roughness coefficient or Manning’s n is a measure of the resistance to flow in a channel. The factors that
influence the magnitude of the resistance to flow include the character of the bed material, cross-section irregularities, depth of
flow, vegetation, and channel alignment. A reasonable evaluation of the resistance to flow in a channel depends on the 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).
D5388 − 21
3.2.12 velocity head (h )—), n—in ft(m), compute velocity head the square of the average velocity divided by twice the
v
acceleration due to gravity measured in ft(m) and computed as follows:
αV
h 5 (9)
v
2g
where:
α = velocity-head coefficient,
V = the mean velocity in the cross section, ft/s (m/s), and
g = the acceleration of gravity, ft/s/s (m/s/s).
4. Summary of Test Method
4.1 The step-backwater test method is used to indirectly determine the discharge through a reach of channel. The step-backwater
test method needs only one high-water elevation and that being at the upstream most cross section. A field survey is made to define
cross sections of the stream and determine distances between them. These data are used to compute selected properties of the
section. The information is used along with Manning’s n to compute the change in water-surface elevation between cross sections.
For one-dimensional and steady flow the following equation is written for the sketch shown in Fig. 1:
h 5 h 1h 1hf1ho 2 h (10)
1 2 v v
2 1
where:
h = elevation of the water surface above a common datum at the respective sections,
hf = the loss due to boundary friction in the reach, and
ho = the energy loss due to deceleration or acceleration of the flow (in the downstream direction) in an expanding or contracting
reach.
5. Significance and Use
5.1 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 D3858). 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.
6. Interferences
6.1 The cross sections selected should be are typical and representative of the reach half way to each adjacent cross section. If
there are abrupt changes between adjacent cross sections, the results could be suspect. The ratio of the conveyance to the
conveyance at an adjacent cross section should stay is within 0.7 and 1.4.
6.2 Care must be taken in selecting the water-surface elevation for the downstream cross section. It should not be so high that it
would reflect The elevation is too high if it reflects backwater at the upstream cross section or soand t
...