Investigation of the Perfect Hydraulic Jump in Horizontal Rectangular Channel

Accelerating the process of transition from supercritical to subcritical flow, by formation a forced hydraulic jump at the contract section (Forced perfect hydraulic jump), is one of the most important measures, in decreasing flow velocity, water energy dissipation and alleviation the scouring problem, leading to lessening the required protection length against the erosion issues in the bed of downstream of the channel. In the current study, physical model was prepared precisely at fluid mechanics laboratory in the faculty of Engineering/Alkhums at Elmergib University. Comprehensive experiments were conducted to evaluate measured and calculated characteristics of the perfect free jump, and consequently, the existence of the perfect hydraulic jump is investigated. Eventually, equation was derived that might be used to guarantee the existence of a free perfect jump, which is the limiting condition between both repelled and drowned jumps as well as, the limiting condition between both repelled and drowned jumps was graphically found.


INTRODUCTION 1.Hydraulic jump and water energy dissipation
Studying hydraulic jump issues started to raise after the early 19 th century. The hydraulic jump was connected with the Momentum Principle by Belanger in 1828. experiments were carried out by researchers and results showed excellent verification of the Momentum Principle in the hydraulic jump [1]. Whenever the flow profile changes from supercritical to subcritical, standing wave is formed which is called hydraulic jump. As a result, the water surface in the channel abruptly raised, turbulent water zone is generated, resulting in formation of surface rollers with intensive water mixing and air entrainment, accompanied by dissipation of a huge amount of water energy [2]. Hydraulic jump might be categorized in two types in regarding to characteristics of their bed, the first one is a classical hydraulic jump with smooth bed, and the other type is a forced hydraulic jump. The type of classical hydraulic jump has been widely studied by many researchers [3,4].

Hydraulic structure and the hydraulic jump
Hydraulic structures are commonly constructed in streams of erodible bed materials, or soil of fine particles and easy to transport due to flowing water, such as silt and clay. In the events of heavy rainfall, massive amount of surplus water might be released from the reservoir within a short space of time, through weirs, spillways and gates of the hydraulic structures, producing flow of high velocity. Accordingly, supercritical flow of high turbulent zone is generated, downstream the channel, immediately behind the toe of the hydraulic structure, causes a bed shear stress, resulting in, significant increase in sediments movement downstream of the hydraulic structure. consequently, the level bed of the channel in this zone becomes corroded and this is commonly known as local scour, as shown in Figure 1. Continuous erosion can deteriorate the foundation of the structure and maybe leading to the failure of the whole structure by time or in severe weather conditions [5].

MATERIALS AND METHODS 2.1 Experimental set-up
The experiments were performed at fluid mechanics laboratory in the faculty of Engineering/Alkhums at Elmergib University. The model was installed, and the experiments were conducted specially for studying the parameters involved in ‫العلىم‬ ‫األسمريت:‬ ‫الجامعت‬ ‫مجلت‬ ‫والتطبيقية‬ ‫األساسية‬ Journal of Alasmarya University: Basic and Applied Sciences counter flow dissipator on the formed jump, considering the three cases; Free perfect jump, forced perfect jump and drowned jump, as shown in Figure 2 [6]. The numbered accessories of the experimental setup may be described in details as following:

Experimental investigation in characteristics of the perfect free jump
Different values of discharges flowing over the spillway crest were tested; W Q = 500, 1000, 1500, 2000 and 2500 cm 3 /sec, and the five corresponding values of the headwater depths; H = 45.7, 46.98, 48.05, 48.98 and 49.85 cm, respectively. Utilizing the tailgate in the flume, the formed hydraulic jump can be forced to move towards the toe of the spillway and located at the contracted section. In this case, the formed hydraulic jump is called perfect one ( 1 y = c y ). The sequent depths 1 y and 2 y , as well as the length J L of the formed jump were measured. The required measured and calculated data are depicted in table 1 and 2, respectively, where the characteristics of the free perfect hydraulic jump condition are described.   Table 2. Calculated data of the perfect free jump.   To guarantee the formation of the free perfect jump, the head / tailwater depth ratio 2 y H have to have a certain value, such a value might be assessed as follows: The discharge passing through the contracted section W Q , may expressed as: where v C is the velocity coefficient and B is the channel width.
The velocity of the headwater approach 0 v may be found as: Consequently, Froude number 0 F , is given as: From which:

Condition of a free perfect hydraulic jump
As stated, the head / tailwater depth ratio 2 y H , that guarantee the existence of a free perfect jump, may be found from equation (9). The experimental measurements were used to verify equation (9), as shown in Table 3 and

CONCLUSION
The free perfect jump is that jump condition which separates between both repelled and drowned jumps. The values of 2 y H calculated from equation (9), will guarantee the existence of a free perfect jump, which is the limiting condition between both repelled and drowned jumps. Forcing the formed hydraulic jump downstream hydraulic structures as much as possible towards the toe of the structure is imperative, as it is in the case of the perfect hydraulic jump in the current study, resulting in, shortening the required length of downstream bed protection to a large extent and finally reducing the cost of construction. Therefore, verification of creation and existence of the perfect hydraulic jump is important matter in hydraulic structures field.