The sluice gate discharges water into a horizontal channel with velocity of 6m/s and depth of flow is 0.4m, the width of the channel is 8m. Determine whether Hydraulic jump will occur and if so find its height and loss of energy per kg of water. Also determine Power lost in the hydraulic jump.

Given,

Velocity of flow $(V_1)$ = 6m/sec

Depth of flow $(y_1)$ = 0.4 m

Bed width (b) = 8m

• $Discharge$ $per$ $unit$ $width$ $(q) = {Q \over b} = {A_1V_1 \over b} = {by_1 * V_1 \over b} = V_1*y_1 = 2.4$ $m^3/sec$
  
  
• $Froude's\ number\ (F_r)\ = {V_1 \over {\sqrt {gy_1}}} = 3.028\ \gt\ 1.$
  
  

• If $F_r$ is greater than 1, then the flow changes to super critical to sub critical.
• Hence, the hydraulic jump may occurs.
  
  

• $Depth\ of\ hydraulic\ jump\ (y_2) = {y_1 \over 2} [\sqrt {1 + 8F_r^2} - 1]\ = 1.525\ m.$

Therefore,

• $Height\ of\ jump,\ (H) = y_2 - y_1 = 1.525 - 0.4 = 1.125\ m.$
  
  

• $Loss\ of\ energy\ per\ Kg\ of\ water\ (h) = {(y_2 - y_1)^3 \over 4y_1y_2} = {(1.525 - 0.4)^3 \over 4*1.525*0.4}\ = 0.5835\ m$
  
  

• $Discharge\ (Q) = AV = 19.2\ m^3/sec$

$Therefore,$


$Power$ $loss$ $(P)$ = ${pQh \over 1000}$ $kw$ $= {9810 * 19.2 * 0.5835 \over 1000}$ $= 109.9$ $Kw$ $Ans.$