The horizontal to vertical side slope in the case of a Cippoletti weir is 1:4.

Explanation:
A Cippoletti weir is a type of flow measuring structure used in open channel hydraulics to measure the flow rate of water. It consists of a rectangular or trapezoidal notch with a V-shaped opening in the center.

The horizontal to vertical side slope refers to the ratio of the horizontal distance to the vertical distance between the sides of the weir. In the case of a Cippoletti weir, the horizontal distance is four times the vertical distance.

This side slope ratio is important because it affects the flow characteristics of the weir. A steeper side slope would result in a narrower and deeper channel, while a flatter side slope would result in a wider and shallower channel.

The 1:4 side slope ratio for a Cippoletti weir is based on empirical studies and is commonly used in practice. This ratio provides a good balance between channel width and depth, allowing for accurate flow measurement and minimizing the potential for flow disturbances.

The V-shaped opening in the center of the weir allows for a more gradual contraction of flow compared to a sharp-crested weir, reducing energy losses and flow disturbances. The flow over the weir crest can be measured using various methods, such as the velocity-area method or the head-discharge relationship.

In conclusion, the horizontal to vertical side slope in the case of a Cippoletti weir is 1:4. This ratio is based on empirical studies and provides a good balance between channel width and depth for accurate flow measurement.