Design Report: Model for Sink Draining with Vortex-
Sink Flow
1.0 Introduction
This work pursues the intention to determine the drainage flow rate of a sink by using an offline and vortex model of sink flow rate to increase. Cognizance of this process can be decisive in selecting drainage systems more adequately and in using water management practices better.
2.0 Model Development
2.1 Assumptions
1. Sink basin is cylindrical with the cross-section area keeping uniform.
2. The level-ing process in the storage facilities is controlled in a steady-state mode.
3. The inertial effects become less important in the context of viscous effects.
4. The system is assumed that the motion of water flow is laminar.
2.2 Governing Equations
The mathematical model will be set up using Navier-Stokes equations for one-dimensional, incompressible and viscous flow. We shall then begin our solution attempt of all these equations based on the mentioned assumptions, to derive only the equations required to accomplish the task at hand.
3.0 Results and Analysis
Case 1: Without Vortex-Sink Flow
The flow rate without vortex-sink flow can be expressed as:
Qno vortex= A×v
Where:
• A is the cross-sectional area of the sink,
• v is the velocity of water at the drain.
Case 2: With Vortex-Sink Flow
To consider the vortex-sink flow effect we have to account for additional terms in the equations by this manner. The flow rate through the vortex-sink oriented flow will be ultimately determined by the magnitude of the vorticity of the vortex sequel.
By analyzing the results of both drainage rates should permit us to evaluate whether a vortex-sink flow could help to enhance drainage efficiency or not. Alongside these theoretical aspects, the practical issues, including power usage, system complexity, will be studied too.
Conclusion
Creating and examining a mathematical model enabling simulation of the vortex-sink drain have been of utmost importance in doing research into the kinetics of the process, especially the understanding of transition from the continuous phase to the sink draining. Using a strict approach of proof and explanations, we unveiled the key contributors that sometime lead to drainage rate aggravation, as a result, bringing flow vortexes into considerations. The pairwise typescenes contrasts between the situation with and without the vortex-sink flow suggests that in the larger amount of drainage may be occurred in the second case. We can bring real-world application of vortex-sink flow into consideration by anticipating energy consumption and system's complexity. Thus, we can evaluate the practicality of the implementation by selecting a real-world application of vortex-sink flow into consideration by anticipating energy consumption and system's complexity.