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AREA =

WETTED

PERIMETER

HYDRAULIC

RADIUS = AREA/WP

Z = 1

Z = 4 PLUS

Q = C/n) A R = C/n) A R h2/3/3 S 0

1/2/2

Manninganning s Equation forEquation forOpen Channel Flowpen Channel Flow

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ManningManning s Formula calculates ans Formula calculates anaverage velocit yaverage velocity

V = (C/n) RV = (C/n) R hh 2/32/3 SS 001/21/2

ManningManning ssFormulaFormulacalculates ancalculates an

averageaverage velocityvelocity

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Mannings Coefficient n )

Mannings Coefficient n )

ExamplexampleDetermine the average velocity of flow andetermine the average velocity of flow andchannel top width for a parabolic shapedhannel top width for a parabolic shapedchannel having a flow depth of 3.9 feet, ahannel having a flow depth of 3.9 feet, achannel slope of 0.8 percent and ahannel slope of 0.8 percent and aroughness coefficientoughness coefficient n = 0.03. The0.03. Therequired crossequired cross -sectional area is 50 ftectional area is 50 ft 2 .ALSO, determine the channel dischargeLSO, determine the channel discharge Q )..

d = 3.9 ft 3.9 ft

slopelope s ) = 0.008 = 0.008n = 0.03 0.03A = 50 ft 50 ft 2

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D = d + freeboard = d + freeboard

Example --- Solution

From Table:

R = 2 d / 3 = 2 3.9) / 3 = 2.6 ft

V = C/n) R h 2/3 S 0 1/2

V = 1.49/0.03) 2.6) 2/3 0.008) 1/2

V = 8.4 ft/sec

Q = A * V = 50 ft 2 * 8.4 ft/sec = 420 ft 3/sec

Example 8.3

A waterway is lined with short grassand has a trapezoidal cross section. Ithas a bottom width of 6 feet, whichmatches the construction equipmentavailable, a channel slope of 0.5percent, and side slopes of 10:1 toensure ease of crossing. It is to carry aflow of 50 ft 3/sec with a freeboard of0.5 feet. What are the total depth andwidth including freeboard) for thischannel?

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Example

IN THIS CASE, AS IN MOST CHANNE LSELECTION PROBLEMS, THE SOLUTIONIS TRIAL AND ERROR.

b = 6.0 ft, Z = 10, Q= 50 ft 3 /sec

s = 0.005 ft/ft

Mannings Coefficient n )

Mannings Coefficient n )

n = 0.05 = 0.05D = d + freeboard = d + freeboard

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Examplexample ----- Solutionolution

For use in the Manningor use in the Manning s Formula, theFormula, theslope is 0.005,lope is 0.005, n = 0.05. Properties from0.05. Properties fromTABLE 8.1. Z = 10, q = 50 ftABLE 8.1. Z = 10, q = 50 ft 3/s, b = 6.s, b = 6.

AREA = b d + Z dREA = b d + Z d 2 = 6.0 d + 10 d 6.0 d + 10 d 2

Rh = AREA / P AREA / P

V = 1.49/0.05) R = 1.49/0.05) R h2/3/3 0.005)0.005) 1/2/2 and Q= V*And Q= V*A

05102061210206122 .*.. d d Z d bP

Examplexample ----- Solutionolution

AREA = 6.0 d + 10 dREA = 6.0 d + 10 d 2

R = AREA / P = AREA / P

V = 1.49/0.05) R = 1.49/0.05) R 2/3/3 0.005)0.005) 1/2/2

Q = V*A = 50 ft = V*A = 50 ft 3 /secse c

05.10*20.6 d p

46.00118.561.1346.2052.002.00

44.00105.031.0744.1947.501.9042.0092.491.0242.1843.201.80

40.0080.920.9740.1739.101.70

38.0070.290.9238.1635.201.60

36.0060.550.8736.1531.501.50

34.0051.700.8234.1428.001.40

33.6050.030.8133.7427.321.38

32.0043.680.7732.1324.701.30

30.0036.470.7230.1221.601.20

28.0030.030.6728.1118.701.10

26.0024.330.6126.1016.001.00

Top,ftQ,calcRh , ftPer, ft Area, ft 2

Quess d,ft

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Example 8.3xample 8.3

b = 6.0 ft, Z = 10, Q = 50 ft = 6.0 ft, Z = 10, Q = 50 ft 3 /secsec

s = 0.005 ft/ft = 0.005 ft/ft

depth = 1.38 ftepth = 1.38 ftwith freeboard D = 1.38+ 0.5 = 1.88 ftith freeboard D = 1.38+ 0.5 = 1.88 ft

T == 44.04.0 ftt

VEGETATED WATERWAYSEGETATED WATERWAYS

Examples:xamples:drainage from fieldrainage from field

terraces orerraces ordiversionsiversions

roadside drainageoadside drainageditches.itches.

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