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Manning’s Equation
and the Internal Combustion Engine
Douglas J. Trieste
The internal combustion engine was invented
in 1859. It consists of an engine block, pistons, intake and exhaust
values, carburetor, crank shaft, flywheel, etc. It was based on
the combustion of a mixture of fuel and air expanding in a cylinder,
moving a piston, and turning a crankshaft. It’s main nemesis were
friction and heat loss. Since that time, there have been many refinements
and improvements, but the basic design remains the same. Most improvements
have come about by variation on a theme. There has been honing
and refining, but it is still the same basic design. Is there no
other way to make an internal combustion engine, or are the concepts
and principles used in 1859 still the best that we can do in today’s
world?
In a like fashion, Manning’s equation
for open channel flow was developed in 1889 and remains in use today.
The general Manning equation is:
in which
Q = the discharge (ft3/s); A = cross-sectional area (ft2); R = the
hydraulic radius (ft); S = the energy gradient, and n = Manning’s
roughness coefficient.
Manning’s equation was based on data
from flume studies and developed for uniform flow conditions in
which the water-surface slope, friction slope, and energy gradient
are parallel to the streambed, and the cross-sectional area, hydraulic
radius, and depth remain constant throughout the reach. Today,
the Manning equation is probably the most popular for practical
open-channel flow computations, including hydraulic computer models.
It is easy to use, gives results that range from reasonable to accurate
in many situations, and is accepted by the industry. It has served
us well for many years and is to be commended.
However, the results from the Manning
equation are essentially at the mercy of n-values. And the
selection of appropriate n values is as much an art as a science.
Many sources offering guidance are available on n selection. Some
of these include Barnes (1967), Benson and Dalrymple (1967), Chow
(1959), Limerinos (1970), and, Jarrett (1985). But, due to the
variability found in nature, it is difficult, if not impossible,
to accurately estimate n in complex hydraulic situations.
Manning’s equation is commonly used
in natural channels for conditions that are not consistent with
that from which it was developed. These conditions include non-uniform
reaches, unsteady flow, irregular shaped channels, turbulence, steep
channels, sediment and debris transport, moveable beds, etc. It
is assumed that the equation is valid in these conditions, and the
energy gradient adjusted via roughness coefficients (n-values) to
make the equation as accurate as possible. As a result, much research
as been performed on n-values.
Most improvements pertaining to the
Manning equation have come about by variation on a theme – the original
design of the Manning equation remains an industry standard. Only
the “theme” (n-values) is changed to improve its performance.
We work on making “Volkswagon improvements” on n-values –
honing, shaping, defining, etc. But, even the famous and ever popular
Volkswagon Bug was eventually discontinued for new and different
models that combine and integrate all that has been learned and
developed. Is it best to keep refining what we have? Or, would
we be ahead to develop new equations that would eventually give
better results?
Can no better equation than the Manning equation be developed, or are
the concepts and principles used in 1889 still the best today?
It is
interesting to wonder that if the Manning equation, or, piston-based
internal combustion engine as we know it were never developed, then
what would we use today?
Is it possible to replace the Manning
equation with something new and different that draws upon all the
knowledge that we learned since its development? The Manning equation
is at the mercy of n-values which are a black box (Trieste
and Jarrett, 1987) in many situations. The equation itself is rarely
challenged, but n-values are continually debated. Could
there be a better approach?
Is it time to develop new concepts in
engines to better meet future needs such as mechanical efficiency,
simplicity, fuel type and consumption, pollution, and costs? And,
is it time to develop new open-channel flow equation to better solve
continual nemesis in computation such as non-uniform channels, unsteady
flow, large floods, high-gradient channels, unstable beds, sediment
and debris transport, supercritical/subcritical flow regimes, etc.?
This
paper in no way intends to discount the Manning equation or internal
combustion engine, but to provide food for thought on improvement
of old designs, versus development of new designs.
References
Barnes, H.H., Jr., Roughness Characteristics
of Natural Channels, U.S. Geological Survey Water-Supply Paper 1849,
1967.
Benson, M.A., and Tate Dalrymple,
General Field and Office Procedures for Indirect Discharge Measurements,
U.S. Geological Survey, Techniques of Water-Resources Investigations,
Book 3, Chapter A-1, 1967.
Chow, V.T., Open Channel Hydraulics,
New York, McGraw-Hill, 1959.
Jarrett, R.D., Determination of Roughness Coefficients
for Streams in Colorado, U.S. Geological Survey Water Resources
Investigations Report 85-400, 1985.
Limerinos, J.T., Determination of the Manning Coefficient
from Measured bed Roughness in Natural Channels, U.S. Geological
Survey Water-Supply Paper 1898-B, 1970.
Trieste and Jarrett, ASCE Proceeding
of a Conference, Irrigations Systems for the 21st Century, Portland,
Oregon, July 28-30, 1987.
Douglas J. Trieste was a Hydraulic Engineer, Bureau of Reclamation,
Denver, CO when he wrote this article. Presently he is the owner
of Flow Technologies, Lakewood, CO; (303) 989-1427; dtrieste@msn.com.
The original article was published in W.H. Espey, Jr, and P.G. Combs
(editors), Proc. of 1st International Conf., Water Resources Engineering,
American Society of Civil Engineers, San Antonio, TX, Aug. 14-18,
1995, Vol. 1, pp. 76-78. Copyright (c) 1995 ASCE; Reproduced by
permission of the publisher (ASCE). (www.pubs.asce.org)
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