What is the resistive force without considering buoyancy?

[charlies1902]

Homework Statement

Attached.

I am working on part (i). What is the resistive force?

Shear stress= μ*(du/dy) = μU/l = F/A

Since the force is up and down, it causes a shear stress, thus area is parallel to the force and thus it is the 4 faces B*L

Thus, A=4*B*L

→ F=μ*U*A/l = 4*μ*U*L*B/l

Where = viscosity
l=clearance gap
L=length of block
F=Resistive force
A=Area

I'm not sure if that is the correct method. Can someone please verify?

 

[Chestermiller]

Looks good. The fluid in the gap exerts a vertical shear force on the 4 vertical sides of the block. Looks like the analysis is right on target.

 

[charlies1902]

Okay thanks, the second part asks me to find the "terminal velocity"

This is what I did

F=4*μ*U*L*B/l=ma
m=ρV
Where ρ is the density of the solid, not the fluid
and V is the volume of the block = (B^2)*L

Plugging that in and simplifying I got U=ρ*B*g*l / (4*μ)

I'm a bit hesitant on that answer because it did not involve the density of the fluid. Is this the correct method?

 

[Chestermiller]

No. There is an upward (buoyant) force from the surrounding liquid acting on the block, equal to weight of the displaced liquid ρ_liqVg. So the net downward force from the weight of the block combined with the upward (buoyant) force from the surrounding liquid is equal to...?

 

[charlies1902]

No. There is an upward (buoyant) force from the surrounding liquid acting on the block, equal to weight of the displaced liquid ρ_liqVg. So the net downward force from the weight of the block combined with the upward (buoyant) force from the surrounding liquid is equal to...?

Oh, I think I'm supposed to ignore that. The problem stated to neglect buoyancy. Is that still necessary?