Final answer:
The b) Froude number represents the gravitational force acting on the fluid in gravity-driven flow problems, while the Reynolds number determines whether the flow is laminar or turbulent based on fluid characteristics such as velocity, density, and viscosity.
Step-by-step explanation:
In the context of gravity-driven flow problems, the parameter that represents the gravitational force acting on the fluid is the Froude number. The Reynolds number, on the other hand, is a dimensionless parameter that indicates whether the flow is laminar or turbulent. It is calculated based on the fluid's velocity, characteristic length (such as diameter), density, and viscosity. The viscosity of a fluid is the measure of its resistance to gradual deformation by shear or tensile stresses, and it directly affects viscous drag, which is the resistance force exerted on a moving object within the fluid. When calculating the Reynolds number, the unitless nature of this number can be shown by substituting the units for velocity, characteristic length, density, and viscosity and then cancelling the units out. Viscous drag is affected by several factors including the velocity, the area of the plate moving through the fluid, the distance between plates in a flow, and the coefficient of viscosity. As velocity increases and/or viscosity decreases (with other factors being consistent), there is a transition from laminar flow to turbulent flow, indicated by an increase in the Reynolds number.