Step 1: Identify the Fluid Control Research Institute.
The Fluid Control Research Institute (FCRI) is a government scientific body located in Palakkad, Kerala. It specialises in testing, calibration, and certification of fluid control equipment such as valves, pipes, and flow meters.
Step 2: Identify its parent ministry.
FCRI functions under the Ministry of Heavy Industries, Government of India, which oversees public sector industrial enterprises and engineering research bodies.
Step 3: Eliminate wrong ministries.
Ministries of Earth Science, Agriculture, and Chemicals do not oversee FCRI. It correctly falls under the Ministry of Heavy Industries.
\[ \boxed{\text{Ministries of Heavy Industries}} \]