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 (μa and μb) of the two fluids related?

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

Answer 1

The density of fluid A is greater than the density of fluid B because the force required to move the plate is directly proportional to viscosity

Step-by-step explanation:

Based on the provided information, we can determine that the force required to move the bottom plate in contact with fluid A is twice the force required to move the bottom plate in contact with fluid B. The force required to move the plate is directly proportional to the coefficient of viscosity, n, as stated in the given equation. Therefore, we can conclude that the density of fluid A (μa) is greater than the density of fluid B (μb) because the force required to move the plate is directly proportional to viscosity.