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 roughness

Estimate Manning roughness for each of the following flow events:
Merced River at Happy Isles Bridge near Yosemite CA, May 17, 1950
Middle Fork Flathead R. near Essex MT, May 22, 1948
Pond Cr. near Louisville, KY, Feb. 14, 1950

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.

C. Comparison of Manning n under varying flow conditions at a station

Another way to use the Manning equation is for the calculation of n when v, R and S are known. In X2partC.xls are data for three different flow events at Tobesofkee Creek near Macon, Georgia (cross section 11) and two different flow events at Provo River near Hailstone, Utah. Set up a spreadsheet in Excel, or get X2partC.xls from SSIL or the web. Do the following calculations for each flow event. In your interpretation, refer to the photos and diagrams for each site (on reserve in the Map Library; soon on the web).

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 Manning’s 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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