Calculating Shear Stress on Parallel Plates at 15 deg C

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SUMMARY

This discussion focuses on calculating shear stress on parallel plates in laminar flow at 15 degrees Celsius. The velocity distribution is defined by the equation \(\frac{u}{u_{max}} = 1 - (\frac{2y}{h})^2\), with parameters set for water, where \(u_{max} = 0.10 m/s\) and \(h = 0.25 mm\). The shear stress is calculated using the formula \(\tau_{yx} = \mu \frac{du}{dy}\) with a dynamic viscosity \(\mu = 1.14 \times 10^{-3} N \cdot s/m^2\). The final calculated shear stress on the upper plate is \(-1.82 N/m^2\).

PREREQUISITES
  • Understanding of laminar flow principles
  • Familiarity with shear stress calculations
  • Knowledge of fluid properties at different temperatures
  • Basic calculus for differentiation
NEXT STEPS
  • Study the derivation of the velocity profile for laminar flow between parallel plates
  • Learn about the effects of temperature on fluid viscosity, specifically for water
  • Explore advanced shear stress calculations in non-Newtonian fluids
  • Investigate computational fluid dynamics (CFD) simulations for flow analysis
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This discussion is beneficial for mechanical engineers, fluid dynamics researchers, and students studying fluid mechanics, particularly those focusing on laminar flow and shear stress calculations.

falcon0311
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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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I've got it figured out. [tex]-1.82 N/m^2 = \tau_{yx}[/tex]
 
seems correct
 

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