How Does Fluid Friction Affect Motion on an Incline?

[Nenad]

I'm working on a fluid mechanics problem and I am not too sure how to approach it. There is a system with an inclined plane and 2 cubes, one attached to the other via a massless string and run through a massless pulley. One cube is dangeling down the vertical edge and the other is on the incline. They both weigh the same amount. The incine is 30 degrees and the question asks to calculate the tension in the string and the terminal velocity of the cubes. The incline is covered with a thin 0.1mm thick layer of oil which has a density of 886kg/m^3 and a dynamic viscosity of 0.29N s/m^2. The information it gives me is that the cubes specific gravity is 2.7 and the side dimentions are 20cm. The oil distribution can be considered to be linear.

I have it set up as a classical mechanics question, but not having any previous experience in fluids, I need to know what kind of force the fluid wil make with the Cube on the incline. I figure that there will be a shear stress. I have No idea how to calculate this. The rest of the problem I know how to set up. Is this shear stress calculated as a constant and then treated like kinetic friction, or is it considered a force? If someone could just quicky give me a quick explination and an equation or two on how to claculate the force exerted by the fluid, that would be great.

Regards,

Nenad

 

[Nate810]

The force exerted by the fluid on the cube will be determined by the velocity of the cube and the viscosity of the fluid. Generally, the force is given by the equation F = μv, where μ is the dynamic viscosity of the fluid and v is the velocity of the cube. In this case, the force will be given by F = 0.29N s/m2 * v. The velocity of the cube can be determined from the equation v = gsin(30°)t, where g is the acceleration due to gravity (9.81 m/s2) and t is the time it takes for the cube to reach its terminal velocity. Knowing the terminal velocity, you can then solve for the tension in the string using the equation T = mgsin(30°) + μv, where T is the tension in the string, m is the mass of the cube, and μ is the dynamic viscosity of the fluid.

 

[thepatientmental]

Hi Nenad,

Thank you for reaching out for help with your fluid mechanics problem. Friction caused by a fluid is a common topic in fluid mechanics and can be approached using several different methods. In this case, it seems like you are on the right track by setting up the problem as a classical mechanics question.

To calculate the force exerted by the fluid on the cube on the incline, you will need to consider the shear stress caused by the fluid. Shear stress is defined as the force per unit area that a fluid exerts on an object as it flows over it. In this case, the fluid is oil, which has a density of 886kg/m^3 and a dynamic viscosity of 0.29N s/m^2. The oil is also distributed linearly on the incline.

To calculate the shear stress, you can use the equation τ = μ(dv/dy), where τ is the shear stress, μ is the dynamic viscosity, and dv/dy is the velocity gradient in the direction perpendicular to the incline. Since the oil is distributed linearly, the velocity gradient will also be linear. You can use the equation dv/dy = Δv/Δy, where Δv is the change in velocity and Δy is the change in height on the incline.

Once you have calculated the shear stress, you can use it to determine the force exerted by the fluid on the cube. This force will act in the opposite direction of the motion of the cube on the incline. You can then use this force, along with the weight of the cube, to calculate the tension in the string and the terminal velocity of the cubes.

I hope this helps and gives you a better understanding of how to approach the problem. If you need further assistance, don't hesitate to reach out for more help. Good luck with your problem!