| dc.description.abstract | An air concentration probe has been developed which is ideally suited for measurements in a jump.
Complete air concentration studies of the jump have been made for nine Froude numbers from 2.42 to 11.72.
It has been shown that:
(a) The mean air concentration CCC at different sections in a jump increases rapidly in the initial portion to a maximum value CmaxC_{\text{max}}Cmax , and then falls off gradually in the latter portion of the jump.
(b) The maximum mean air concentration CmaxC_{\text{max}}Cmax is given by the equation:
Cmax=f F11.35C_{\text{max}} = f \, F_1^{1.35}Cmax =fF11.35
(c) The location of the section of maximum mean air concentration, expressed as xd1\frac{x}{d_1}d1 x , increases rapidly with F1F_1F1 , reaching a maximum value of 1.70 at F1=5.0F_1 = 5.0F1 =5.0, and then falls off rapidly, becoming almost constant for values of F1F_1F1 greater than about 8.0.
The ratio of air discharge to water discharge (calculated on the basis of certain assumptions) increases rapidly in a certain initial length of the jump, termed the air intake zone L1L_1L1 , and falls off gradually in the latter portion of the jump, known as the air release zone L2L_2L2 .
(a) The lengths of the air intake zone and the air release zone, when expressed in dimensionless form, have been shown to depend only on the Froude number F1F_1F1 .
(b) The maximum value of ppp, denoted as pmax p_{\max}pmax , can be taken as the maximum air driving capacity of the jump (in a closed conduit) and is given by:
pmax =0.018(F1 1)p_{\max} = 0.018 (F_1 - 1)pmax =0.018(F1 1)
The distribution of the air concentration for the nine Froude numbers for the full body of the jump has been analysed.
A critical analysis of the controversy on the length of the hydraulic jump has been given, along with the proposal of two new rational criteria.
Based on a mean air concentration of two percent, the length of the jump has been presented.
It has been shown that the residual mean air concentration at the end of the jump (the end being fixed by the Bradley-Peterka curve) is given by the appropriate derived equation.
Pre entrained Jump Studies
The pre entrained jump has been defined, along with a Froude number applicable to aerated flows.
A rational theory for pre entrained jumps has been presented.
An approximate equation has been developed for calculating the energy of aerated flows.
An expression has been developed for the energy loss in the pre entrained jump.
Experimental Studies
This chapter presents the experimental investigations on pre entrained jumps for values of air entrained Froude numbers from 2.60 to 5.59.
The validity of the flow equation formulated in Chapter 5 has been verified.
The correlation of the energy loss equation is only fairly satisfactory.
From the limited experimental data, it can be concluded that the pre entrained jump is not useful for removing air from air pockets.
The basic assumption regarding the neglect of entrained air at the end of the pre entrained jump has been shown to be permissible.
Further Findings
Based on the author's findings, the flow equation of the pre entrained jump has been developed in a form suitable for assessing the effect of air entrainment on stilling basin performance.
This equation has been solved using the experimental results of Straub and Anderson for a sanded boundary.
It has been shown that the additional sequent depth requirement of the pre entrained jump over that of the normal jump-expressed as a percentage, i.e., ( 1)�0(\lambda - 1) \times 100( 1)�0-is independent of the Froude number for 10<F1<2510 < F_1 < 2510<F1 <25.
It has been shown that ( 1)�0(\lambda - 1) \times 100( 1)�0 is less than about 10 percent for 0< 0<0.340 < \Theta_0 < 0.340< 0 <0.34 and increases rapidly for higher values of 0\Theta_0 0 , reaching 53 percent for 0=0.70\Theta_0 = 0.70 0 =0.70.
For spillways with roughness similar to that used by Straub and Anderson, and for terminal flow conditions, the additional sequent depth requirement is always less than 10 percent for discharge intensities from 30 to 1000 cusecs per foot width.
Based on these findings, and rational arguments, the observed fact that prototype hydraulic jump basins designed from model studies perform satisfactorily despite self aeration not accounted for in models is established.
Miscellaneous Contributions
A flow profile equation has been developed that fits the mean velocity profile for Froude numbers 5 to 12.
An improved design method for sunk type stilling basins has been presented.
A design chart has been evolved for direct determination of basin depth.
A similar direct design solution has been presented for baffle type basins.
It has been shown that at the air inception section, the Froude number has a critical value dependent on boundary roughness.
Simple slide rule methods have been developed for computing alternate depths in rectangular channels.
A two parameter table has been prepared for critical depth computation in trapezoidal channels.
A rational conversion formula between Manning抯 nnn and Nikuradse抯 ksk_sks has been developed, along with a table of ksk_sks values for common channel surfaces.Abstract Not Available | |
