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TRAPEZOIDAL AND CIRCULAR CHANNEL ANALYSIS HYDROCALC HYDRAULICS MANUAL. PAGE 16 <br />T =Top width of flow (feet) O <br />r =Radius of Channel (feet) ~ <br />F =Depth of Flow (feet) <br />2.1.3 EXAMPLES OF NORMAL DEPTH PROCEDURE <br />2.1.3.1 Computing Normal Depth in a Trapezoidal Channel <br />E,~rample 6-4 of Chow's "Open Channel Hydraulics" (Chow 1959) relates to the computation of <br />Normal Depth in a trapezoidal channel. The channel fn the example has a bottom width of 20 <br />feet, side slopes of 2:1, a Mannfng's roughness coefficient of 0.025, and a required flow capacity <br />oC 400 cfs. <br />: <br />:. <br />; <br />~ <br />~ <br />~ <br />~ <br />. <br />. <br />:::.:::.~:.:: ~.,:. <br />.~.:::;:;~~~';.:'.:':_~.::~:~::. <br />.~ ..~..:~::..~.. <br />:~:~:.:..~::::.,:.~NORMAIr:.DEP TH~ CO[~.UTATION~::'~:.~:-.:':...~..: ~~~~:~~::'::~ ~:': <br />. ..:. <br />: ~:~~~~:~,.`:~:~:-::::.:::r':~:::'::::::,::: <br />~~.:~~~~:~:'~:':... <br />. <br />Flow'Rate culsid::feet'. er :second :.:::.:::::. ::.':,:::.::.";;,:::;";:;: ::.:::`..:::::: <br />„ .. . ,..... (. <br />. P. .. '.400...'., :.':.:;:::;:.:::;."::.::.:?: <br />. <br />channel:Bottogi 51o.e:tfeet':.er.:foot}..:.';.::::::;:`::.:.:.:.::.'""':::::.::':: '0:016::.:~.::':::::.:::''.;;::.:;. <br />,.. <br />,. <br />nns.. ou essCoefficent. n-v 1ue:.'>:::.:.:.:.;:':..>.::::-';. <br />Ma in4 <br />R <br />9 a <br />: <br /> <br />.'0:025.;.:;::<::.:;.::';::. <br />.: <br />. <br />: <br />~,:,_. <br />. ~.~:....:::Chansiel~.~Side.Slo I;eft":.Side~~::..(hozontal~/vertically',::.: <br />. ....::: <br /> <br />'~;2~:::,:;.:::::~:~~~::~::°:;::::::~::::::':':~;: <br />. <br />............:......... . <br />. .:..... <br />..... ...Channel:~::side.:Sl.ope~;;::.::~Ftigfit.:;side..:~:(hq;izontaJ%,vetscal): <br />.... <br />~.:.2~:s:;~~..;';:~?';<";:;:;`.;;:.'.t:~ <br />; <br />;: <br />.: ....:.:~:..~.~Channel~.:.8ottom:~~Wfdtli:;~ feet};:~:.::::~~''::..:.:~::.~:i':~:::.::;:~;:;.~;::':::r:.:::'.:.;:~~::.:.':~ :.::::::.:..::.:::.:. : <br />.:~.20:;;:r':;:::.`~:~:~'::.;::~~~~:~~~%°:?'::'~':::. <br /> <br />;'D H~:: FEET ~::~:'i::i::r'::.~.'::::..::~::..:;.::'.:;::.:::::•..::::..;:.:<.:;;':.:`.:.:,:'..':;;: "':::'::~~:::~~::; <br />NORMAL <br />~.~.:... ...~ <br />'~ <br />~ <br />EPT . <br />( : <br />. <br />.. <br />: . <br />. <br />. <br />.... ....... ... ... ... ... .r .~:~ <br />e ~.: a .:..g~ ... <br />..:. .:~.:~:.':"F1ow~:~~Ve~loai~tY.~.,(fe t p r.,s ond)':~~:~~:~~::~~:-::::~:::~:~.~::::'::.:~~:::~~::~:~:~:;::':..:~';:~~~~~ <br />:~~~~4.~.:.45.::::.:::',,.~::~.:::'.:::~~~~:::: <br />:~~ ..: <br />.~::. ~.. ~.:. :~. ov :~Number:~'::~. ~..:...~ ..,..::..::~:.~: ~:;~..::~~:::.~.:~.. ~:.~•.;.::~.< ::::.:.....::~.:.. :~:~..~..::.. <br />:::.Fr ..,.:: 0'.479~~~!:::.~~'.~'.:~:1':~~~:I:` <br /> <br />, <br />.. <br />.~: ...:.:~::.:. elo t ~~ ead.:~~ feet...::~::~:~:~~..:,.:::~~..:~ ::..::.:::::.~:; :...:::::.:~; ~..::.~:.~:,:.:~:;~:,~:.~::::~~~~~::~.,~~: <br />,V ci y.. H. ( ). . <br />:~~:::'.:~0~:~31:~.:::::i:::::~:.::::'.~;;,":.c.; <br />..... ..... <br />... ..:~~:::~Ener ~ Head:~(feet ~ ~ . . <br />~.3~~67.:~:;.,...:.r::'~:::;~:~.~.':::~:~ <br />:~:..:.:::;; <br />.~ ~~:~.... ~::.:~:::~~:cross-Sectional~:Area ~ £.~.Floi+:.':(square. feetl::~:::~~, <br />'~:~.~:~~ <br />.~~ <br />:. <br />:~~~: :~::fl4r:g.3`;;::::::::';;;:::'.;'~:::~:::'. <br />.~ <br />. <br />. <br />. <br />. <br />,. <br />..... . ... . <br />•• .T.op.:Width of..Flo ,.,.(f tl ........::.:..:.:..:... <br />;:.. <br />' : <br />,. <br />.. . . <br />:...,. <br />:: <br /> <br /><Enter>-''.'Re eat::::'<R>ertor.:.cEec>.::.End^.' .:.:.:... <br /> <br />P .. Pa.. ~.:.. . <br /> <br /> <br />.:::.::.5::r::;:;:::%.:'::;.:::'. <br /> <br />~. <br /> <br />1 <br /> <br />Fgure 2-3 Example of Norma! Depth in irapezoidd Channel ll <br />t <br />Chocks manual computations indicate that the Normal Depth of flow !n the channel under the <br />stated conditions is 3.36 feet. As indicated Ln Figure 2-3, theTrapezoida] Channe]AnalysLsprogrsm <br />provides exactly the same result. The computed flow velocity also agrees very well with the value <br />computed by Chow. Chow computed a flow velocity of 4.46 fps, whereas the program computes <br />a value of 4.45 fps. <br />2.1.3.2 Computing Normal Depth in a Circular Channel <br />As an e.~cample of the Norma] Depth procedure for a circular channel, assume that a clroular pipe <br />culvert 8 Ceet in diameter connects two stormwater detention basins. The culvert has a bottom I <br />slope of 0.01 feet per foot, and the Manning's roughness coefficient for the pipe is assumed to be . <br />0.015. The Normal Depth of (low in the culvert is to be determined for a flow rate of 400 cis. <br />0 1989 Dodson & Associates. Inc.. 5629 FM 1960 West. Suite 314. Houston, Tex 77069. (713) 440-37H7. All Rights Reserved <br />