The hydraulic gradient theory of weir design was developed by Darcy and Beresford.

Introduction
The hydraulic gradient theory of weir design is an important concept in civil engineering, specifically in the design of weirs. Weirs are structures built across rivers and canals to control the flow of water and to measure its discharge. The hydraulic gradient theory provides a theoretical basis for designing weirs that ensure accurate measurement of flow rates.

Development by Darcy and Beresford
The hydraulic gradient theory of weir design was developed by Henry Darcy and William Beresford in the 19th century. Henry Darcy was a French engineer who conducted extensive research on fluid mechanics, particularly on the flow of water in pipes and channels. William Beresford was an English engineer who also made significant contributions to the field of fluid mechanics.

Theory
The hydraulic gradient theory states that the flow rate over a weir is directly proportional to the head of water above the weir crest and the square root of the hydraulic gradient. The hydraulic gradient is the slope of the water surface upstream of the weir. According to the theory, the flow rate can be calculated using the following formula:

Q = k * H * sqrt(S)

Where:
Q is the flow rate,
k is a constant,
H is the head of water above the weir crest, and
S is the hydraulic gradient.

Implications for Weir Design
The hydraulic gradient theory has important implications for the design of weirs. It suggests that in order to accurately measure flow rates, the head of water above the weir crest must be measured and the hydraulic gradient must be determined. This information can then be used to calculate the flow rate using the formula mentioned earlier.

Conclusion
In conclusion, the hydraulic gradient theory of weir design was developed by Henry Darcy and William Beresford. This theory provides a theoretical basis for designing weirs that ensure accurate measurement of flow rates. By considering the head of water above the weir crest and the hydraulic gradient, engineers can calculate the flow rate and design weirs that effectively control and measure the flow of water.

D should be the answer according the explanation