# Calculating Shear Stress in a Fluid Mechanics Problem

• Nenad
In summary: The shear stress equation is based off of the definition of shear stress for a Newtonian fluid. You need the kinematic viscosity, which is the viscosity multiplied by the density. Additionally, you need the velocity, the thickness of the layer, and the viscosity of the fluid.
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

Viscosity = 256.94 Pas

Friction due to shear stress, F = 102776v

Cube mass, m = 21.6kg

$$m g (1 - Sin \theta) = 102776v$$
v = 4.0988ms-1

how did you get that viscosity? and the constant for the hear stress equation. If you could please expliain, I would really appreciate it.

Regards,

Nenad

You were given the kinematic viscosity, you need the simple viscosity, which is the kinematic viscosity multiplied by the density.

The shear shress equation is based on the definition of shear stress for a Newtonian fluid.
Tau = mu*v/z

so shear stress is in opposition to the motion, just like friction right. And could you also ezplain what the vriables are in the shar stress equation. I know the questions I'm asking are simplistic, but I need a definite answer. Thanks in advance.

Regards,

Nenad

Shear stress opposes relative motion in the fluid.

Tau = shear stress; mu = viscosity; v = velocity; z = thickness of layer.

Hope this helps.

thanks a lot speed. I really appreciate the help.

Regards,

Nenad

## 1. What is friction caused by a fluid?

Friction caused by a fluid, also known as fluid friction, is the resistance to motion that occurs when an object moves through a fluid, such as air or water.

## 2. How is fluid friction different from other types of friction?

Fluid friction is different from other types of friction, such as static or kinetic friction, because it occurs between a solid object and a fluid, rather than between two solid objects.

## 3. What factors affect the amount of friction caused by a fluid?

The amount of friction caused by a fluid is affected by several factors, including the speed of the object, the viscosity (thickness) of the fluid, and the surface area of the object.

## 4. What are some examples of fluid friction in everyday life?

Some examples of fluid friction in everyday life include the resistance experienced while swimming, the drag force on a moving car, and the air resistance on a flying airplane.

## 5. How is fluid friction important in scientific research and engineering?

Fluid friction plays a crucial role in many scientific and engineering applications, such as designing efficient aircraft and vehicles, understanding the behavior of fluids in pipes and channels, and studying the movement of ocean currents and weather patterns.

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