The discharge Q in a triangular weir is determined by various factors, including the head (H) of fluid flow. The relationship between the discharge and the head can be expressed as Q ∝ H^2.5.

Explanation:
1. Relationship between discharge and head: The discharge of fluid through a triangular weir depends on the head of fluid above the weir. The head is the difference in elevation between the water surface and the crest of the weir.

2. Discharge formula: The discharge Q through a triangular weir is given by the Francis formula, which is derived from theoretical considerations and experimental data. The formula can be expressed as Q = C * L * H^2.5, where Q is the discharge, C is a coefficient, L is the length of the weir crest, and H is the head of fluid flow.

3. Power relationship: The exponent of 2.5 in the formula indicates a power relationship between the discharge and the head. This means that as the head increases, the discharge increases at a faster rate.

4. Factors affecting the exponent: The exponent in the discharge formula can vary depending on the shape of the weir. For a triangular weir, the exponent is typically 2.5. This is because the triangular shape of the weir causes the velocity of fluid flow to increase more rapidly with increasing head compared to other shapes.

5. Experimental validation: The relationship between discharge and head has been experimentally validated for triangular weirs. Numerous tests and studies have shown that the discharge varies as H^2.5 for this particular shape.

In conclusion, the discharge Q in a triangular weir varies as H^2.5. This relationship is derived from the Francis formula and has been experimentally validated. The exponent of 2.5 indicates a power relationship between the discharge and the head, with the discharge increasing at a faster rate as the head increases.