Let's go through each governing law and its corresponding application to find the correct pair:
- Hagen Poiseuille law (Option A): The Hagen Poiseuille law describes the flow of a viscous fluid through a pipe. It relates the pressure drop across the pipe to the flow rate, pipe radius, and viscosity of the fluid. This law is indeed related to pressure drop, so option (A) is correct.
- Rittinger's law (Option B): Rittinger's law is a law that describes the relationship between the energy required for size reduction and the size of the particles being crushed. It is related to the energy required for size reduction, not vapor pressure. Therefore, option (B) is incorrect.
- Stefan Boltzmann law (Option C): The Stefan Boltzmann law relates to the amount of radiation emitted by a black body to its temperature. It states that the total energy radiated is proportional to the fourth power of the temperature. This law governs radiation heat transfer, so option (C) is correct.
- Raoult's law (Option D): Raoult's law deals with the vapor pressure of a solvent in a solution and does not apply to size reduction. Therefore, option (D) is incorrect.
Thus, the correct governing laws and their corresponding applications are:
- (A) Hagen Poiseuille law - Pressure drop.
- (C) Stefan Boltzmann law - Radiation heat transfer.
Final Answer:
\[
\boxed{\text{(A) Hagen Poiseuille law - Pressure drop, (C) Stefan Boltzmann law - Radiation heat transfer}}.
\]