Hirt 



Fig. 4 - Velocity vector plot for the sluice 

 gate calculation shown in Fig. 3 



Another interesting flow occurs when fluid piles up against a rigid wall and 

 forms a hydraulic jump. The jump conditions relating uniform states of flow on 

 either side of a hydraulic jump are easy to derive — they are conservation of 

 mass and momentum. Kinetic energy decreases in the transition. The lost en- 

 ergy usually reappears as fluid turbulence. At very low Reynolds numbers, 

 however, there can be enough viscous dissipation in a laminar transition to 

 preclude the development of turbulence. Figure 5 shows a laminar jump at Reyn- 

 olds number 4.33 (based on incoming fluid depth and speed relative to the jump). 

 Fluid is input at the right-hand boundary and piles up at the left boundary, which 

 is a rigid wall. A hydraulic jump is traveling back to the right. Clearly, the 

 flow is laminar. The overshoot in elevation and a slightly low jump speed are 

 believed to be caused by a failure to satisfy correctly the tangential stress con- 

 dition of Eq. (23). When the Reynolds number exceeds about 10, the free-surface 

 approximations discussed in the section on Free -Surface Boundary Conditions 

 are satisfactory. 



Fig. 5 - A hydraulic jump calculation at Reynolds number 4.33 



428 



