POWER November 2020 - 27

HYDROPOWER
accurately quantify Manning's equation
is clearly demonstrated.
The term S(g) is the slope times gravitational
acceleration. As the slope, d(y)/dx,
becomes larger, there is a larger gravitational
force acting to accelerate the flow.
As mentioned before, Manning's
equation is an average of all the openchannel
equations published prior to
1889. The fact that it did not include the
effect of the velocity head correction factor
is quite understandable. It was not
until as late as 1877 that the Coriolis velocity
head correction factor was recognized
to be a variable and not a constant.
The relationships of Equation 2 show
Manning's n is a metric for the velocity
head correction factor, that is, n is proportional
to α1/2. Theoretically, if n is doubled,
the velocity head correction factor is increased
fourfold and the average velocity
is halved. This is the mechanism through
which the roughness of the fluid boundaries
acts to retard the flow velocity across
an infinitesimally thin cross-section.
As noted, Manning's n is directly affected
by the hydraulic radius (R7/24). This
does show that selecting a Manning's n
is not only a function of roughness, but
of the cross-sectional shape of the water
course. The fact that canals may exhibit
some differences in Manning's n due to
their shape alone, as well as their roughness,
has been previously documented
in other literature.
In a paper titled " Determination of Rugosity
Coefficient for Lined and Unlined
Channels " published by the Karnataka
Engineering Research Station in India, it
says, " Flow in channels is complicated by
the fact that the form of roughness elements
and hence the resistance to flow
are functions of the characteristics of
channel shape and alignment. These factors
make up the coefficient of rugosity
or the roughness coefficient. " The reason,
as mentioned before, is the smaller the
hydraulic radius, the greater the relative
percentage of the volume of flow that is
in direct contact with the given absolute
roughness of the boundary. Therefore,
the greater the drag that the boundary imposes
to retard the volumetric flowrate,
the more non-uniform the velocity profile
becomes, as calculated by α. Thus, the
smaller the hydraulic radius, the greater
the energy loss. Conversely, the greater
the hydraulic radius, the more the velocity
profile tends to become uniform over the
cross-section. Coincidently, Chezy's C is
inversely proportional to R1/8.
The equations developed by Chezy
and Manning may appear to be very simple;
h owever, they represent complex
interactions of hydraulic parameters of
fluids in open channels. The experimental
process presented in this article may
be used to study these interactions. The
use of this experimental method, on the
very limited and narrow basis described
above, suggests that the difference
between Chezy's and Manning's equations
may not be as great as it appears.
The real difference may be more in the
degree of dependence that each coefficient
of flow resistance has on the
velocity head correction factor and the
hydraulic radius. ■
-Lee H. Sheldon, PE is a hydropower engineer
with 50 years of experience. He has
published 33 technical papers and a college
textbook on hydropower engineering,
and has worked on every federal hydroelectric
project in the Pacific Northwest,
among others. He was formerly a professor
at OIT, where he taught hydropower
engineering and fluid mechanics.
Content Licensing for Every Marketing Strategy
Marketing solutions fit for:
Outdoor | Direct Mail | Print Advertising | Tradeshow/POP Displays | Social Media | Radio & TV
Leverage branded content from POWER Magazine to create a more powerful and
sophisticated statement about your product, service, or company in your next marketing
campaign. Contact Wright's Media to find out more about how we can customize your
acknowledgements and recognitions to enhance your marketing strategies.
For information, call Wright's Media at 877.652.5295 or visit our website at www.wrightsmedia.com
November 2020 | POWER
www.powermag.com
27

http://www.wrightsmedia.com http://www.powermag.com

POWER November 2020

Table of Contents for the Digital Edition of POWER November 2020