Geog 427/527: Fluvial Geomorphology
Winter 1999, University of Oregon
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[Go to Method for estimating Manning's n] [Go to photos and cross-sections for each site]
Exercise 2: Flow and Resistance
Due Date: Thursday, Jan. 28 in class.
The Manning equation is used to estimate discharge, and to determine roughness. The equation can be used in two ways. If dimensions of the channel cross-section are available but measurements of velocity are not, Manning n is estimated from channel characteristics and velocity is calculated using the Manning equation. Alternately, if field measurements of channel width, depth and velocity are available, the Manning equation can be used to calculate roughness (n). We will try both approaches, to become familiar with the Manning equation and with values of n. A. Estimation of Manning roughnessEstimate Manning roughness for each of the following flow events:
Use the reach map, cross section diagrams and photos for each
site to estimate n. These are located on the web and on reserve in the Map Library. Also,
use the channel descriptions below.
Description of channels:
Merced R. at Happy Isles Bridge near Yosemite CA: Fairly straight channel is
composed of boulders with trees along top of banks (D50 = 253 mm; D84
= 550 mm). Judging from the cross section and photos, the flow event probably just barely
reached into the base of the trees.
Middle Fork Flathead R. near Essex MT: Bed consists of boulders (D50 =
142 mm; D84 = 285 mm). Banks are composed of gravel and boulders, and have
trees and brush along the tops. Judging from the cross section and photos, the flow event
probably just barely reached into the base of the trees.
Pond Cr. near :Louisville KY: Bed is fine sand and silt. Banks are irregular with
fairly heavy growth of 2- to 8-inch trees on the banks above low water (i.e., inundated at
high water), particularly on left bank. Bridge abutment forms constriction at section 3.
At Pond Creek, judging from the cross-section diagrams, the water surface in the event
probably reached a few feet below the feet of the man shown in the photo.
Estimate roughness using the method described in the accompanying material (Arcement and Schneider, 1989). Do this by hand, or set up a spreadsheet for the n calculations if you prefer. For each site, show the value you chose for each component of n, a word or phrase indicating why you chose that value, and the total n value.
[Go to Method for estimating Manning's n] [Go to photos and cross-sections for each site]
B. Calculation of Manning roughness Using the data in the table below, calculate Manning roughness for each of these flow events from Part A.standard form of the Manning equation: V = (1.49/n)(R0.67S0.5) for feet/sec
to calculate n: n = (1.49/V)(R0.67S0.5)
Note: In an Excel formula, to raise a number to a power use the operator ^. For example, Yx is written (Y^x).
| x-sect. | area (sq. ft.) |
top width (ft.) |
mean depth (ft.) | hydraulic radius (ft.) | mean velocity (ft./sec.) |
length between sections (ft) | fall between sections (ft.) |
| Merced River at Happy Isles Bridge near Yosemite CA, May 17, 1950 | |||||||
| 2 | 263 | 64 | 4.1 | 3.98 | 7.41 | 200 | 3.40 |
| Middle Fork Flathead R. near Essex MT, May 22, 1948 | |||||||
| 2 | 1658 | 187 | 8.87 | 8.73 | 8.75 | 291 | 1.07 |
| Pond Cr. near Louisville, KY, Feb. 14, 1950 | |||||||
| 2 | 830 | 122 | 6.8 | 6.48 | 1.78 | 90 | 0.05 |
Part B question:
B1. Compare your estimated values of n from Part A with the calculated n values from this
section. Assume that the calculated value from Part B is more accurate. For each site,
redo your estimate of n, showing which components you would change and why.
Turn in your worksheet showing calculations for parts A and B. Answers for part A will be
evaluated in terms of consistency and correct application of procedure, rather than
whether the answer is numerically correct.
1. Calculate slope using the length and fall.
2. Calculate n, using the Manning equation.
date |
Q, cfs |
mean depth, ft |
hydraulic radius, ft |
velocity, ft/sec |
length, ft |
fall, ft |
|
| Tobesofkee Cr., sect. 11 | 3/7/58 |
2540 |
8.0 |
7.29 |
3.63 |
731 |
0.58 |
| Tobesofkee Cr., sect. 11 | 2/6/59 |
2240 |
7.6 |
6.8 |
3.58 |
731 |
0.58 |
| Tobesofkee Cr., sect. 11 | 2/9/59 |
1260 |
5.6 |
5.0 |
3.36 |
731 |
0.60 |
| Provo R., sect. 5 | 6/13/52 |
1200 |
3.1 |
3.02 |
6.95 |
109 |
1.04 |
| Provo R., sect. 5 | 10/7/52 |
64.8 |
1.1 |
0.82 |
1.9 |
109 |
0.84 |
Note that the event on the Provo River is the higher of the two events shown in the cross-section diagrams. The man in the photo is indicating the flow level with the horizontal rod.
[Go to Method for estimating Manning's n] [Go to photos and cross-sections for each site]
Part C question:
C1. How does n vary with Q at Tobesofkee Creek near Macon, Georgia? At Provo River near
Hailstone, Utah? Based on what you can see in the photos, why are these two stations
different?
Turn in your spreadsheet showing calculations and n values.
Sources:
Barnes, H. H., J., 1967. Roughness characteristics of natural channels. U. S. Geological
Survey Water Supply Paper 1849. (All cross-section data are from this source.)
Arcement, G.J., Jr., and Schneider, V.R., 1989. Guide for selecting Mannings roughness coefficients for natural channels and floodplain. U. S. Geological Survey Water Supply Paper 2339.
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last update: 02/12/07 10:45 PM
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