FLOOD03351

• County: Statewide
• Basin: Statewide
• Title: Engineering and Design Hydraulic Design of Flood Control Channels
• Date: 7/1/1991
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

and

+ yQ2 = m3 + yQ2
m2 + mp ~ QA3

Combining these equalions results in

ml + yQ2 _ [(Ap ) ( yQ2 )] = m2
gA'l lAi" 19A'l
2 2
+mp+yQ =m3+yQ
~ 9A3

This reduces to the Koch-Qustanjen equation

ml - mp + yQ2 (Al _ Ap) = m2 + yQ2
gAt ~
2
-m3-m + yQ
p 9A3

where

y = specific weight of water, pOlmds
per cubic foot (pet)

Q = total discharge, cfs

ml = total hydrostatic force of water in
upstream section, lb

ml = total hydrostatic force of water in
pier section, lb

m3 = total hydrostatic force of water in
downstream section, Ib

I11p = total hydrostatic force of water on
pier ends, Ib

AI = cross-sectional area of upstream
channel, square feet (f2)

A, = cross-sectional area of channel
- within pier section, f2

A3 " cross-sectional area of downstre:lm
channel. f2

(2-19)

(2-20)

(2-21)

EM 1110-2-1601
1 Jul 91

Ap = cross-sectional area of pier
obstruction. fr-

(g) Curves based on the KochCarstanjen equation
(Equation 2-21) are illuslI:lled in Plate l2a. The resulting
now profiles are shown in Plate 12b. The necessary
computations for developing the curves are shown in
Plate 13, The downstre:lm depth is usually known for
tranquil-flow channels and is greater than critical depth.
It therefore plots on the upper branch of curve ill in
Plate 12:1. If this depth A is to the right of (greater force
than) the minimum force value B of curve II, the flow is
class A and the upstre:lm design depth C is re:ld on curve
I immediately above point A. In this case, the upStre:lm
depth is cona-olled by the downstream depth A plus the
pier cona-action and expansion losses. However, if the
down= depth D plots on the upper branch of curve
ill to the left of (less force than) point B, the upStre:lm
design depth E is that of curve I immedialely above point
B, and critical depth within the pier section B is the con-
lrOl The downstre:lm design depth F now is that given
by curve ill immediately below point E. A varied now
compuction in a downStre:lm direction is required to
determine the location where downstre:lm channel condi-
tions effect the depth D.

(h) In rapid. flow channels, the now depth UpSlre:lm
of any pier effect is usually known. This depth is less
than critical depth and therefore plots on the lower branch
of curve 1. If this depth G is located on curve I to the
right of point B, the now is class C. The downslre:lm
design depth H and the design flow depth within the pier
section I are re:ld on curves ill and II. respectively, im-
mediately above depth G. A varied flow computation is
required to determine the location where downStre:lm
channel conditions again conlrOl the depth. However. if
the unaffected upStre:lm rapid-now depth J plots on the
lower branch of curve I to the left of point B, the design
upstre:lm depth K is read on curve I immediately above
point B. The design downstre:lm depth Lis re:ld on curve
II immediately below point B. In this case, class B flow
results with a hydr:wlic jump between depths J and K
(plate 12b) upslream of the pier as conlrOlIed by critical
depth within the pier section B. A varied now computa.
tion is again required to determine the location where
downsa-eam channel conditions conlrOl the flow depth.

(3) Design charts, rectangular sections. A graphic
solution for class A flow in rectangular channels. devel-
oped by USAED. Los Angeles (1939), and published as
HDC 010-612. is reproduced in Plate 14. The drop in

2.7