THREE -RESERVOIR PROBLEMS CONCEPTS WITH SOLUTION

The video introduces the concept of three-reservoir problems, emphasizing that the principles apply to systems with more reservoirs (e.g., four or five), though they become more complex. The core idea is to understand fluid flow and energy distribution in a system with multiple reservoirs connected by pipes to a common junction.

The discussion highlights that energy conservation and constant discharge are key. The most critical aspect is determining the energy grade line (EGL) at the junction, which dictates the direction of fluid flow. The EGL at the junction considers pressure, velocity, and elevation head. Crucially, the velocity head at the junction is often neglected for simplicity, as its impact is minimal compared to major head losses.

The first example demonstrates how to calculate head losses and discharges when the junction's pressure and elevation are given. The energy at the junction is calculated, and then the head losses between each reservoir and the junction are determined. These head losses are used with the Darcy-Weisbach formula to find the discharge in each pipe. The problem concludes by finding the elevation of the third reservoir and the discharge in its connecting pipe.

The second problem addresses a scenario where the junction's energy head is not directly given. The approach involves assuming the position of the junction's EGL relative to the reservoirs. Based on this assumption, continuity equations are formulated, and individual pipe head losses are calculated. If the initial assumption leads to inconsistencies (e.g., negative square roots), the assumption must be revised. This example illustrates how to calculate the elevation of Reservoir C.

The third and final problem deals with calculating the flow in each of the three pipes when no discharges are given. The primary strategy is to assume the energy head at the junction. This assumption defines the flow directions and corresponding head loss equations. By expressing discharge in terms of head loss for each pipe and using the continuity equation, a system of equations is formed. The video demonstrates how to use a calculator's 'shift-solve' function to find the head losses and, subsequently, the discharges. It also emphasizes the importance of checking assumptions and how to adjust them if the calculation yields an impossible result.