FLOOD06232

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

EM 1110-2-1601
1 Jul 91

velocity head may be used. This method under the same
circumstances may be applied to bridge openings contain.
ing piers.

b. Pier losses. Rapid. tranquil, or a combination of
rapid- and tranquil-flow conditions may occur where only
bridge piers are located in the flow area. Flow through
bridge piers for this condition is classified as class A. B,
or C. according to the depth of flow in relation to critical
depth occurring upstream, between piers, and downstream.
Plate 10 is a graphic description of these classes, which
are discussed below. Plate 11 is useful in determining the
class of flow in rectangular channels.

(I) Class A flow (energy method). Chow (1959,
paragraph 17-10) presents a discussion and several energy
loss formulae with appropriate coefficients that may be
used for computing bridge pier losses for tranquil flow
(class A). While the momentum method presented below
may also be used for class A flow, thc energy method
usually gives better results.

(2) Classes B and C flows (momentwn method).

(a) A graph (example shown in Plate 12) constructed
from the equation proposed by Koch and Carstanjen
(Chow 1959) and based on the momentum relation can be
used for determining graphically the flow classification at
constrictions due to bridge piers. In addition, the graph
can be used for estimating unknown flow depths. A
summary of the equation derivation follows.

(b) In a given channel section the momentum per
unit time of the flow can be expressed by

M = ~ l ~V)

(2.12)

where

M = momentum per unit time, pounds (lb)
(from pounds-second per second
(lb-sec/sec))

~ = momentum correction coefficient

'Y = specific weight of water, pounds per
cubic foot (pel)

Q = total discharge. cfs

2-6

v = average channel velocity. feet per
second (fps)

e

g = acceleration of gravity, ft/sec2

In Equation 2-12 ~ is generally assumed to be equal to
1.0. Since

Q = AV

(2-13)

Equation 12 can be written

.

2
M = 'YQ
gA

(2-14)

(c) The total hydrostatic force m (in pounds) in the
channel section can be expressed as

m = riA

(2-15)

where y is the distance from the water surface to the
center of gravity (centroid) of the flow section.

e

(d) Combining Equations 14 and 15 results in

2
m+M=riA+J!2-
gA

(2-16)

By the momentum principle in an unconstricted channel

.

2
ma ,+ 'YQ
gAa

'YQ2
+-
gAb

(2-17)

= mb

where ma and mb are the total hydrostatic forces of
water in the upstre.am and downstream sections,
respectively, lb.

(e) Based on experiments under all conditions of
open-channel flow where the channel was constricted by
short, flat surraces perpendicular to the flow. such as with

e