Calculating Surface Shear Stress in a Boundary Layer with Given Velocity Profile

In summary, the conversation discusses finding the surface shear stress in a boundary layer given the velocity and distance from the surface. The equation used is τ = μ(du/dy) and the constants a and b are solved for using the given velocity data. The final answer is 1.17 N/m^2.
  • #1
exphaze
4
0

Homework Statement


If the velocity v of the air in a boundary layer having a dynamic viscosity of
18x10-6 kg/ms is given in terms of the distance y from the surface by v = ay + by2

where a and b are constants, calculate the surface shear stress if at 1.5 mm from the surface the velocity is 75 m/s, and at 3.0 mm from the surface it is 105 m/s.

Homework Equations


τ = μ(du/dy)

The Attempt at a Solution

 
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  • #2
What have you figured out so far?
 
  • #3
Chestermiller said:
What have you figured out so far?
I have tried the differences of the velocities and distance (du/dy) . Then multiplied it by the dynamic viscosity which came out as 0.36 N/m^2 but the answer is apparently 1.17 N/m^2.
 
  • #4
exphaze said:
I have tried the differences of the velocities and distance (du/dy) . Then multiplied it by the dynamic viscosity which came out as 0.36 N/m^2 but the answer is apparently 1.17 N/m^2.
You need to solve for a and b from the velocity data; a is the shear rate at the wall.
 
  • #5
Chestermiller said:
You need to solve for a and b from the velocity data; a is the shear rate at the wall.
I have worked out a = 50000 and substituted to τ*shear rate =μ and this came out as 0.9 N/m^2. I am still stuck.
 
Last edited by a moderator:
  • #6
exphaze said:
I have worked out a = 50000 and substituted to τ*shear rate =μ and this came out as 0.9 N/m^2. I am still stuck.
I get a = 65000/sec
 
  • #7
Chestermiller said:
I get a = 65000/sec
I got it now, Thanks for the advice!
 
  • #8
Hello
I have the same issue, but unfortunately I can't solve it.
any hind please?
 

Related to Calculating Surface Shear Stress in a Boundary Layer with Given Velocity Profile

1) What is fluid mechanics?

Fluid mechanics is the branch of physics that deals with the study of fluids in motion, including air velocity. It involves the study of how fluids behave under different conditions and the forces that act on them.

2) How is air velocity measured in fluid mechanics?

Air velocity is usually measured using an anemometer, which is a device that measures the speed and direction of airflow. There are different types of anemometers, such as hot-wire anemometers, pitot tubes, and vane anemometers, each with their own specific method of measurement.

3) What factors affect air velocity in fluid mechanics?

There are several factors that can affect air velocity, including the density and viscosity of the fluid, the shape and size of the object the fluid is passing over, and the presence of any obstacles or turbulence in the flow.

4) How does air velocity impact the behavior of a fluid?

The velocity of air can significantly impact the behavior of a fluid. Higher air velocities can increase the kinetic energy of the fluid, causing it to flow faster and potentially creating turbulence. Lower air velocities can also affect the flow of a fluid, such as causing stagnant areas or reducing the mixing of different fluids.

5) What are some practical applications of fluid mechanics involving air velocity?

Fluid mechanics and air velocity have many practical applications, including in aerodynamics, weather forecasting, air conditioning and ventilation systems, and the design of aircraft and vehicles. They are also important in understanding air pollution and air quality.

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