Aeration experiments, maintaining nappe flow conditions, were carried out on a rectangular stepped cascade of total height 3.0 m to determine the total number of steps, slope of the entire cascade and hydraulic loading rate at which maximum overall aeration efficiency occurs, keeping the surface area of individual steps constant. Based on dimensional analysis, the overall aeration efficiency at standard conditions (E20) was expressed as a function of square of total number of steps (N2) and dimensionless discharge (dc/h), where dc and h represent critical depth in a rectangular prismatic channel and individual step height respectively. An empirical equation with E20 as the response and N2 and dc/h as the independent parameters was developed based on the experimental results subject to 36 ≤ N2 ≤ 196 and 0.009 ≤ dc/h ≤ 0.144. The experimental results showed that the overall aeration efficiency (E20) for a particular step height of stepped cascade increases with increase in dc/h up to a certain value and then decreases. This may be due to at higher dc/h, i.e., at higher hydraulic loading rate, the flow approaches the transition zone and thereby aeration efficiency decreases. E20 was also found to increase with number of steps at any hydraulic loading rate, because of the increased surface area of fall. The optimum number of steps, slope of the entire stepped cascade and hydraulic loading rate were found to be 14, 0.351 and 0.009 m2/s respectively producing the maximum value of overall aeration efficiency of 0.90.
Imaging terrestrial planets with a free-flying occulter and space telescope: an optical simulation
