ANS:C - 1.84

In open channel flow, particularly in a rectangular channel, the ratio between the critical depth (ycy_cyc​) and the initial depth (y1y_1y1​) where a hydraulic jump occurs is approximately 1.84. Here’s an explanation:

1. Hydraulic Jump: A hydraulic jump occurs in open channel flow when supercritical flow (high velocity, low depth) changes to subcritical flow (low velocity, high depth). This phenomenon is characterized by a sudden increase in flow depth and energy dissipation.
2. Critical Depth: The critical depth (ycy_cyc​) is the depth of flow at which the specific energy (energy per unit weight of fluid) is a minimum for a given discharge. It is a key parameter in determining the characteristics of hydraulic jumps.
3. Ratio of Depths: Empirical studies and theoretical analyses have shown that the ratio of the critical depth to the initial depth (yc/y1y_c / y_1yc​/y1​) when a hydraulic jump occurs in a rectangular channel is approximately 1.84. This means that the flow depth increases by a factor of 1.84 at the location of the hydraulic jump compared to its initial depth.