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Curva de Remanso Direct Step Method. Movimento Gradualmente Variado (MGV). 1. Entenda o que é MGV. 2. Identifique os perfis e tipo de controles – M1, M2, M3, S1, S2, S3, .. 3. Aprenda a desenhar a superficie do remanso. Tipo de superfície da água. Mild Slope – M1, M2, M3 - PowerPoint PPT Presentation
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Movimento Gradualmente Variado (MGV)1. Entenda o que MGV.2. Identifique os perfis e tipo de controles M1, M2, M3, S1, S2, S3, .. 3. Aprenda a desenhar a superficie do remanso.
Tipo de superfcie da guaMild Slope M1, M2, M3Steep Slope S1, S2, S3
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Quando yn> yc ento a declividade mildQuando yn < yc ento a declividade steepQuando yn=yc ento a declividade crticaQuando So=0 (sem declividade) ento yn = Quando So scCritical : yo = yc or so= scMild : yo > yc or so< scHorizontal : S0 = 0Adverse : S0 < 0
Initial depth is given a zoneZone 1 : y > ynThe space above both critical and normal depthZone 2 : yc < y < ynThe region lies between the normal and critical depthZone 3 : y < ycThe lowest zone of space that lies above the channel bed but below both critical and normal depth lines
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Classificao das curvas conforme Ven Te Chow
Determinao de ycExemplo: Vazo de 98,1m3/s com largura de 10 m em um canal retangular.Profundide normal 5m, qual o tip de declividade- mild, steep, critical ??
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Perfil Tpico MildSteepProfundidade normalProfundidade Normal Profundidade crtica
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Perfil Tpico MildSteepM2M3M1Profundidade normalProfundidade normalProfundidade crticaS2S3S1A superficie da gua tem diferenas devido as condies de obstrues a montante ou a jusante
Passos na anlise do perfil da superficie da gua
1. Desenho a declividade (slope)2. Determine slope type yn, yc, So3. Desenhe Critical Depth 4. Desenhe Normal Depth5. Connect Normal Depth to control point.Based on profile type
Mild SlopeCasos
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Exemplo simples Remanso y acima da profundidade normal mild slope Sea LevelChannel/RiverReservoir/SeaNormal DepthRiver Level
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Exemplo simples Remanso y acima da profundidade normal mild slope Sea LevelChannel/RiverReservoir/SeaProfile ?Normal DepthRiver Level
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Exemplo simples Remanso y acima da profundidade normal mild slope Channel/RiverNormal DepthRiver Level
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Exemplo simples Remanso y acima da profundidade normal mild slope Channel/RiverNormal DepthRiver Level
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Exemplo simples Remanso y acima da profundidade normal mild slope Channel/RiverNormal DepthRiver Level
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Exemplo simples Remanso y acima da profundidade normal mild slope Channel/RiverNormal DepthRiver Level
Mild SlopeCasos
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Simple Example Drawdown y above normal depth mild slope Sea LevelNormal DepthRiver LevelChannel/RiverReservoir/SeaPerfil ?
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Simple Example Drawdown y above normal depth mild slope Sea LevelNormal DepthRiver LevelChannel/RiverReservoir/SeaPerfil ?
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Simple Example Drawdown y above normal depth mild slope Sea LevelNormal DepthRiver LevelChannel/RiverReservoir/SeaPerfil ?
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Simple Example Drawdown y above normal depth mild slope Channel/RiverNormal DepthRiver Level
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Simple Example Drawdown y above normal depth mild slope Channel/RiverProfile ?Control PointsNormal DepthRiver Level
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Simple Example Drawdown y above normal depth mild slope Channel/RiverProfile ?Normal DepthRiver LevelControl Points at yc
Mild SlopeCasos
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Channel/RiverNormal DepthRiver Level
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Channel/RiverNormal DepthRiver Level
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Normal DepthRiver Level
Steep Slope
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Simple Example Backwater y above normal depth mild slope Sea LevelChannel/RiverReservoir/SeaNormal DepthRiver Level
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Sea LevelChannel/RiverReservoir/SeaNormal DepthRiver Level
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Channel/RiverNormal DepthRiver Level
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Channel/RiverNormal DepthRiver Level
Steep Slope
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Channel/RiverNormal DepthRiver Level
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Channel/RiverNormal DepthRiver Level
Steep Slope
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Channel/RiverNormal DepthRiver Level
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Channel/RiverNormal DepthRiver Level
Quebra do gradeCombinao de declividades diferentes
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Profile Type MildSteepNormal DepthNormal DepthCritical Depth
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Profile Type MildSteepNormal DepthNormal DepthCritical Depth
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Profile Type MilderMildNormal DepthNormal DepthCritical Depth
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Profile Type MilderMildNormal DepthNormal DepthCritical Depth
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Profile Type MildMilderNormal DepthNormal DepthCritical Depth
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Profile Type MildMilderNormal DepthNormal DepthCritical Depth
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Profile Type SteepSteeperNormal DepthNormal DepthCritical Depth
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Profile Type SteepSteeperNormal DepthNormal DepthCritical Depth
DIRECT STEP METHODBaseado na Equao da Energia
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Existem muitos mtodos para se obter o perfil da superfcie da gua.
Direct IntegrationNumerical IntegrationDirect Step MethodGraphical IntegrationNumerical/Computer Methods
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Direct step methodO Direct step method o mtodo mais simples e aplicvel a canais prismticos.Em geral, o mtodo caracterizado por dividir o canal em pequenos trechos para facilitar os clculos passo a passo at atingir o ponto que queremos.
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Direct Step MethodEquating the total head at the two end section 1 and 2, the following may be written;
y1 + v/2g + z1= y2 + v/2g + z2 + hLE1 + (z1 - z2 ) = E2 + hLE1 + so x =E2 + sf x x (so - sf )= E2 - E1 x = (E2 - E1 )/ (so - sf )Where E1 = y1+v12/2gSf = n2Q2/(A2/R4/3 ) = n2v2/R4/3 Sf = (Sf1+Sf2 )/2
Calculation dx start for Backwater is the highest side. dy/dx=+veCalculation dx start for Drawdown is the lowest side. dy/dx=-ve
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Direct Step MethodUm canal trapezoidal tem base B=8.0m, taludes laterais 2:1, o coeficiente de Mannings n 0.025 e a declividade 0.001 m/m. Se o canal termina em queda livre, faa o perfil da superficie da gua para uma vazo de 30m3/s.Primeiro ache: yn e yc.Profundidade normal yn=3.0m e yc=1.69m Segundo: trace o tipo de perfilComo yn > yc ento o perfil Mild Como dy/dx
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