The correct answer is option 'C' - the Reynold number.

Explanation:
The flow profile of a fluid refers to the way the fluid moves within a tube or channel. It describes the distribution of velocities across the cross-section of the tube.

The Reynold number is a dimensionless quantity that characterizes the flow of a fluid. It is defined as the ratio of inertial forces to viscous forces within the fluid. The Reynold number is given by the formula:

Re = (ρ * v * D) / μ

Where:
- Re is the Reynold number
- ρ is the density of the fluid
- v is the velocity of the fluid
- D is the diameter of the tube
- μ is the dynamic viscosity of the fluid

The Reynold number determines the type of flow that occurs in a fluid. It is used to classify flow as laminar or turbulent.

- Laminar flow: When the Reynold number is below a certain critical value, the flow is laminar. In laminar flow, the fluid moves in smooth, parallel layers with minimal mixing. The velocity profile in laminar flow is typically parabolic, with the highest velocity at the center of the tube and decreasing towards the walls.

- Turbulent flow: When the Reynold number exceeds the critical value, the flow becomes turbulent. In turbulent flow, the fluid moves chaotically, with significant mixing and eddies. The velocity profile in turbulent flow is irregular and varies across the cross-section of the tube.

The Reynold number is a key parameter that influences the flow profile of a fluid. As the Reynold number increases, the flow transitions from laminar to turbulent. In laminar flow, the velocity of the fluid is the primary factor determining the flow profile. However, in turbulent flow, other factors such as surface roughness come into play and affect the flow profile.

Therefore, the correct answer is option 'C' - the Reynold number, as it is the parameter that determines the flow profile of a fluid.