FLOOD04361

• County: Statewide
• Basin: Statewide
• Title: Techniques of Water-Resources Investigations of the US Geological Survey Measurement of Peak Discharge by the Slope-Area Method
• Date: 1/1/1984
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

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MEA8UREMENT OF PEAK DI8CHARGE BY THE SLOPE-AREA METHOD

5

weighted conveyance of each su breach on the
form as shown on figure 7. First, use the two-
section formula given in table 1 to compute
directly the discharge for each two-section
subreach. The computed values will most
lik8ly differ for each subreach. Then, using
the appropriate discharge as the "assumed"
value on the form, complete for each subreach
the computation of the various heads, slope,
and "computed" discharge. The "computed"
discharge will agree exactly with the "assumed"
if computations are made correctly. This
procedure provides an interim check and gives
considerable insight into the transformation
of 8nergy and energy loss from section to section
along the reach. Consistency of results among
the subreaches is made evident,
Use one of the equations shown in table 1
to compute the final value of discharge. These
equations are based on the energy equation
and the Manning equation applied throughout
the reach. The values of k in the equations
are 0.5 if t:.h, is positive and 0 if t:.h, is negative
in the given subreach. The value of t:.h, for
each subreach was determined in the previous
computations and may be used to determine
the values of k in the multisection equation.
After the final value of discharge has been
determined, use that value to compute the
subsection discharges for subdivided sections,
the corresponding velocities, and the mean

velocities for all sections. Enter the compu-
tations in the two columns at the right of the
computation form. Computed velocities should
be compatible with the appearance of the
channel after the flood. Gross errors can be
recognized in some instances if velocities are
greatly different from those expected.

Froude Number

The value of the Froude number should be
computed for each cross section after the final
discharge has been determined. The Froude
number is defined as

V
F=-,
~

(9)

where V is the mean velocity and dm is the
average depth in the cross section.
The Froude number is an index to the state
of flow in the channel. For example, in a
rectangular channel the flow is tranquil if the
Froude number is less than 1.0 and is rapid if
the Froude number is greater than 1.0. The
slope-area method may be used for both tranquil
and rapid flow. The Froude numbers for the
various sections or for subsections of compound
sections should be examined to determine the
state of flow in the reach.

Number of
cro.t",edioM

Table: 1 .-Discharge equations ror use: in slope-area measurements

2

t:.h
K'L K,' [ (A,), (k ]
K, +2gA,' -"I Al 1- )+",(I-k)

Q=K,

3

Y t:.h
Q=K3 KKK' A ' A '
K:(K: LI-,+L'-')+2gA.,,[ -"I (A:) (l-k,-oH"'(A:) (k,-3-kl-oHa,(I-k,.,)]

Multiple
(n)

Q=K.-V Aa;.B' where

4=K' L,_, +K' 4, + K.'L"_2l-"-ll+ K.'L"_ll~
... n KIK2 1f, K2Ka ... K(Jl.-2)K(n-l) K(rt-l)Kn

B= A~~g [ -"I (~~Y (l-k,-,H", (~:)' (k..,-kHH"3 (:tY (k...-kHH . . .

+""-ll (AA. )' (k"_I)_.-k('_2l_('_l))+".(I-k"_ll~)]'
(n-l)