共軛水深，水躍(conjugate water depth, hydraulic jump)

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 明渠水理計算_曼寧公式

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例題

已知條件：y1=0.3m，V1=4.5m/s

Fr1=V1/SQRT(g*y1)=4.5/SQRT(9.81*0.3)=2.6231

依據水躍共軛水深公式：

y2=y1*0.5*[-1+SQRT(1+8*Fr1^2)]=0.9730(m)

依據連續方程式:V1*y1=V2*y2

==> V2=V1*y1/y2=4.5*0.3/0.9730=1.3875(m/s)

Fr2=V2/SQRT(g*y2)=1.3875/SQRT(9.81*0.9730)=0.4491

example

Known conditions: y1=0.3m, V1=4.5m/s

Fr1=V1/SQRT(g*y1)=4.5/SQRT(9.81*0.3)=2.6231

According to the hydraulic jump conjugate water depth formula:

y2=y1*0.5*[-1+SQRT(1+8*Fr1^2)]=0.9730(m)

According to the Continuity equation: V1*y1=V2*y2

==> V2=V1*y1/y2=4.5*0.3/0.9730=1.3875(m/s)

Fr2=V2/SQRT(g*y2)=1.3875/SQRT(9.81*0.9730)=0.4491