In falling head permeability test apparatus, the waterhead at any time instant is equal to Difference in the water level.

The falling head permeability test is a common laboratory method used to determine the permeability or hydraulic conductivity of soil. This test is particularly applicable to fine-grained soils with low permeability, such as clays and silts.

During the falling head permeability test, water is allowed to flow through a soil specimen under a constant hydraulic gradient. The apparatus consists of a permeameter, which is a cylindrical tube filled with the soil specimen, and a water reservoir connected to the permeameter through a standpipe.

The water level in the standpipe is initially higher than the water level in the permeameter. As the test proceeds, water flows through the soil specimen, causing the water level in the permeameter to rise while the water level in the standpipe falls.

Waterhead in the falling head permeability test apparatus is equal to the difference in the water level between the standpipe and the permeameter.

Explanation:
- The waterhead is a term used to describe the height or pressure of water in a system. In the case of the falling head permeability test, it represents the difference in water level between the standpipe and the permeameter.
- As water flows through the soil specimen, the water level in the permeameter rises. This rise in water level is directly proportional to the permeability of the soil.
- The height difference, or waterhead, between the standpipe and the permeameter is measured at regular time intervals during the test.
- By monitoring the change in waterhead over time, the permeability of the soil specimen can be calculated using Darcy's law, which relates flow rate, hydraulic gradient, and cross-sectional area.
- Therefore, the waterhead at any time instant in the falling head permeability test apparatus is equal to the difference in the water level between the standpipe and the permeameter.
- Option A, which states that the waterhead is equal to the difference in the water level, is the correct answer.

Overall, the falling head permeability test apparatus is a valuable tool for determining the permeability of fine-grained soils, and the measurement of waterhead is an essential aspect of this test.