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Derive the expression for the depth of Hydraulic Jump in case of Upstream Froudes number.
1 Answer
written 3.0 years ago by |
Let
V1= Velocity of flow on the upstream side
d= Depth of flow on upstream side
Then Froude Number (Fe)1 on the upstream side of the jump is given by
(Fe)1=V1√gd1.....(i)
Depth of flow after the hydraulic jump is d2 given by,
d2=−d12+√d214+2V21d1g=−d12+√d214(1+8V21gd1)=−d12+d12√1+8V21gd1.....(ii)
But from equation (i),
(Fe)1=V1√gd1(Fe)21=V21gd1
Substituting this value in equation (ii), we get
d2=−d12+d12√1+8(Fe)21=d12(√1+8(Fe)21−1)