Calculating Shear Stress on Parallel Plates at 15 deg C

In summary, The conversation discusses a velocity distribution equation for laminar flow between parallel plates, with the variables being h, u_{max}, and y. The goal is to calculate the shear stress on the upper plate and its direction using the equation \tau_{yx} = \mu \frac{du}{dy} at a temperature of 15 degrees Celsius and a dynamic viscosity of 1.14*10^{-3} N*s/m^2. The final result is a shear stress of -1.82 N/m^2 on the upper plate.
  • #1
falcon0311
29
0
So I've got this velocity distribution for laminar flow between parallel plates.

[tex]\frac{u}{u_{max}} = 1 - (\frac{2y}{h})^2[/tex]

h is the distance between the plates with the origin placed midway between the plates. I'm assuming this is for water flowing at 15 deg C with [tex]u_{max} = 0.10 m/s[/tex] and [tex]h = 0.25 mm[/tex].

I'm supposed to calculate the shear stress on the upper plate and give its direction. I'm trying to figure out how to incorporate these into

[tex]\tau_{yx} = \mu \frac{du}{dy}[/tex] at 15 deg C, [tex]\mu = 1.14*10^{-3} N*s/m^2[/tex] I also know the temperature has to be in Kelvin (288.15K in this case). Anyone willing to give me a push?
 
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  • #2
I've got it figured out. [tex]-1.82 N/m^2 = \tau_{yx}[/tex]
 
  • #3
seems correct
 

1. How do I calculate shear stress on parallel plates at 15 deg C?

The formula for calculating shear stress on parallel plates at 15 deg C is:
τ = μ(du/dy)
Where τ is the shear stress, μ is the dynamic viscosity, and du/dy is the velocity gradient.

2. What is the unit of measurement for shear stress?

The unit of measurement for shear stress is typically expressed in pascal (Pa) or newton per square meter (N/m²).

3. How does temperature affect shear stress on parallel plates?

As temperature increases, the dynamic viscosity of a fluid decreases, resulting in a decrease in shear stress. Therefore, at 15 deg C, the shear stress on parallel plates may be lower compared to other temperatures.

4. What is the difference between shear stress and shear rate?

Shear stress is the force per unit area that is applied parallel to the surface of an object, while shear rate is the change in velocity over a change in distance perpendicular to the direction of the applied force. In simple terms, shear stress is the force causing the movement, while shear rate is the measure of the movement itself.

5. Can the calculation of shear stress on parallel plates be applied to non-Newtonian fluids?

The formula for calculating shear stress on parallel plates assumes that the fluid being measured is Newtonian, meaning its viscosity remains constant regardless of the applied shear rate. For non-Newtonian fluids, the calculation of shear stress may vary and other factors may need to be considered.

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