Question

Two different Newtonian fluids (A & B) are placed between identical sets of parallel plates as shown below. Each pair of plates is separated by the same distance L. Both plates are pulled to the right at a constant velocity V and both top plates are held stationary. The force required to pull the bottom plate in contact with fluid A (Fa) is twice the force required to pull the bottom plate in contact with fluid B (Fb). The only motion occurring in each fluid is caused by the movement of the bottom plate. Based on this observation and ignoring edge effects, how are the densities (rhoa and rhob) of the two fluids related?

A. rhoa=rhob because the force required to move the plate is a function of V and L but not fluid properties
B. rhoa=rhob are unrelated because the force required to move the plate is directly proportional to fluid density
C. rhoa and rhob are unrelated because the force required to move the plate is only a function of fluid viscosity
D. rhoa>rhob but the exact relationship cannot be determined from the information given.

Answer 1

The force required to move the bottom plate in contact with the fluids is only a function of fluid viscosity, not density. Therefore, rhoa and rhob are unrelated to the forces required to move the plates (Fa and Fb).

Step-by-step explanation:

The question pertains to the relationship between the forces required to move two different Newtonian fluids (A & B) and their densities. From the information given, the force required to move the bottom plate is solely a function of the fluid's viscosity and not its density. The force exerted by the fluid on the plates is a result of the internal friction, or the viscosity of the fluid, which resists the movement of the layers of fluid between the plates.

Since the force needed to move plate A (Fa) is double that of the force needed to move plate B (Fb), and assuming identical conditions apart from the fluids' properties, the fluid viscosity of A is greater than that of B. This can be understood from the given equation that force is directly proportional to the viscosity (n).

Therefore, the correct answer is that the densities of fluids A and B (rhoa and rhob) are unrelated to the forces required to move the bottom plates. Hence the option: C. rhoa and rhob are unrelated because the force required to move the plate is only a function of fluid viscosity is the correct relation between the densities of the two fluids based on the given observation and ignoring edge effects.

Answer 2

The relationship between the densities (ρa and ρb) of fluids A and B cannot be determined solely based on the given observation. Therefore, the correct option is D: ρa > ρb, but the exact relationship between the densities cannot be established from the information provided.

Step-by-step explanation:

The force required to move the bottom plate through a fluid is influenced by various factors such as fluid viscosity, density, and the distance between the plates (L), among others. In this scenario, the forces Fa and Fb are related to the fluids' properties but not solely determined by one specific property like viscosity or density.

From the given information, it's clear that the force required to move the plate through fluid A (Fa) is twice the force required in fluid B (Fb). However, this observation doesn't provide a direct relationship between the densities of the fluids. The force required is influenced by both viscosity and density, and it is plausible that the higher force in fluid A might result from its higher density or possibly due to a combination of higher density and other fluid properties.

The provided scenario emphasizes that the force required to move the plate is influenced by fluid properties and their interactions with the moving plate. While a direct relationship between the densities of fluids A and B cannot be concluded solely from the given observation, it is reasonable to infer that the higher force in fluid A (Fa) suggests a higher density compared to fluid B (Fb), but the exact magnitude of this relationship cannot be determined without additional information or experimentation.