Journal of Irrigation and Drainage Engineering

Dropshafts are commonly used as flood discharge structures in urban drainage systems and hydraulic structures. Plunging and vortex flows are the two main flow regimes occurring in the dropshaft with a tangential intake. However, the effects of the intake contraction on the flow regime transition have not been studied. This study aims to present the flow characteristics in the transition process between the plunging and vortex flows in dropshafts, through a series of three-dimensional computational fluid dynamic simulations. With the decrease in the intake contraction ratio, the ratio of rotation and falling velocities along the annular dropshaft wall increases gradually, and the vortex flow can remain a long distance in the vertical dropshaft. The flow regime transition from the plunging flow to the vortex flow is analyzed quantitatively based on two specific velocity ratios of rotation and falling velocities. In addition, for large flow discharges, the effects of intake contraction on the flow rotation performance are more obvious than that for small flow discharges. These findings provide reference for the hydraulic design in dropshaft structures.

Despite many deterministic approaches for the optimal design of a canal already proposed, a methodology capable of considering the risk value when there is uncertainty in flow estimation is still lacking. In real engineering problems, we confront linear programming models in which all included uncertain parameters are fuzzy numbers. In the task of canal design, this assumption is because it involves uncertain parameters (load and resistance) estimated by short historical data and limited knowledge about the environment, respectively. This limitation hinders the usage of probabilistic linear programming approaches because the probability of satisfying a constraint should be known with certainty. This paper provides a new method for solving fuzzy number linear programming problems using the concept of fuzzy risk and Yager’s fuzzy ranking function. The result is used for proposing a novel optimization formula that can aid in rectangular canal design. The application of our insightful new methodology is presented in a stormwater canal design example. The findings presented in this paper will appeal to decision-makers and practicing engineers.

In the task of storm sewer design, the accuracy of the method of choice for estimating the risk value is not a trivial task, because it improves the safety and effectiveness of the entire system. Hence, two methods for risk assessment of a storm sewer in an urban area are presented here. The first method is fuzzy risk analysis, in which uncertainty parameters are treated as fuzzy numbers. To do so, a novel formula to calculate the fuzzy risk of sewer flooding with the aim of implementing the alpha-cut principle when runoff and the Manning roughness coefficients are the only uncertainty parameters, is introduced here. The fuzzy number represents the runoff coefficient obtained from the data from seven rainfall events recorded in an experimental urban catchment. In the second method, the fuzzy numbers are replaced with various associated probability distributions, in which all the possible combinations are considered. Then, the Monte Carlo simulation (MCS) technique calculates the corresponding probabilistic risk of flooding. It is observed that computing the limit values of the MCS produces an interval that closely tracks values of the calculated risk using the fuzzy technique. This means that the fuzzy alpha-cut and MCS methods provide similar results and indicate that the fuzzy method for storm sewer risk assessment has acceptable accuracy (more than 97%). But, the representation of uncertainty and the computation time is different in these methods. Hence, the superiority of one method over another depends on the nature of the problem.

In engineering practice the curve-number method is sometimes inappropriately applied to low-rainfall events, thereby ignoring the dependence of the curve number on the rainfall amount. Lack of adjustment of the curve number for low rainfall can lead to substantial underestimation of runoff, and is particularly problematic in the design of water-quality components of stormwater-management systems. An expression is derived for the minimum rainfall required for the applicable curve number to be within 10% of its commonly cited handbook value, and a procedure is presented for adjusting the handbook curve number to account for low-design rainfall. A realistic example is presented to illustrate the procedure.