**The Exit Gradient in a Barrage**

The exit gradient in a barrage refers to the slope or gradient of the water surface downstream of the barrage structure. This gradient is an important consideration in the design and analysis of barrages as it affects the flow characteristics of the downstream channel. In the case of a barrage, the exit gradient is found to be independent of the following factors:

**1. The Applied Head of Water:**
The applied head of water refers to the height difference between the upstream and downstream water levels. Despite the applied head of water varying, the exit gradient remains unaffected. This is because the exit gradient is primarily determined by the shape and dimensions of the downstream channel and the hydraulic characteristics of the flow. The applied head of water only affects the flow rate through the barrage but does not influence the exit gradient.

**2. The Horizontal Length of the Floor:**
The horizontal length of the floor of the barrage does not have any influence on the exit gradient. The exit gradient is primarily influenced by the downstream channel's slope and roughness, which are determined by the natural topography of the area. The horizontal length of the floor does not affect the slope or roughness of the downstream channel and, therefore, does not impact the exit gradient.

**3. The Depth of Upstream Cutoff:**
The depth of the upstream cutoff, which is the depth of the cutoff wall or barrier provided upstream of the barrage, does not affect the exit gradient. The exit gradient is determined by the downstream channel's slope and roughness, which are independent of the upstream cutoff depth. The purpose of the upstream cutoff is to prevent seepage and erosion, but it does not have any influence on the exit gradient.

**4. The Depth of Downstream Cutoff:**
Similar to the upstream cutoff, the depth of the downstream cutoff, which is the depth of the cutoff wall or barrier provided downstream of the barrage, does not have any impact on the exit gradient. The exit gradient is solely determined by the downstream channel's slope and roughness, which are not influenced by the depth of the downstream cutoff. The downstream cutoff is usually provided to prevent erosion and protect the downstream channel but does not affect the exit gradient.

In conclusion, the exit gradient in a barrage is independent of the applied head of water, the horizontal length of the floor, the depth of the upstream cutoff, and the depth of the downstream cutoff. The exit gradient is primarily influenced by the slope and roughness of the downstream channel, which are determined by the natural topography and hydraulic characteristics of the flow.