• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Fluid mechanics question

  • Thread starter math_04
  • Start date
1. The problem statement, all variables and given/known data

Water at 20 degrees C flows in a 0.8cm diameter pipe with a velocity distribution of u(r) = 5[1-r2/(16x10-6)]m/s. Calculate the shear stress on

(a) pipe wall
(b) at a radius where r = 0.2 cm
(c) at centerline of pipe

2. Relevant equations

Shear stress = viscosity x du/dr

3. The attempt at a solution

So what I did first was get du/dr, which is -10/(16x10-6)r = du/dr

I used the value of viscosity for water at room temperature and pressure which is 1.1x10-3

And then I just plugged everything in so shear stress at wall = 1.1x10-3x -10/16x10-6x0 = 0N/m2 at pipe wall. It is x0 because it is the pipe wall so r = 0m

for part (b) I got 1.1x10-3x (-10/16x10-6) x 0.2x10-2 = -1.38N/m2

Looking at the answers, it seems I got it wrong. part (a) answer is 2.5N/m2 and part(b) is 1.25N/m2

Can anyone please tell me where I got it wrong? Somehow I feel like I made a careless mistake somewhere....

1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
30,835
4,452
Water at 20 degrees C flows in a 0.8cm diameter pipe with a velocity distribution of u(r) = 5[1-r2/(16x10-6)]m/s.

And then I just plugged everything in so shear stress at wall = 1.1x10-3x -10/16x10-6x0 = 0N/m2 at pipe wall. It is x0 because it is the pipe wall so r = 0m
What makes you think r is 0 at the pipe wall? What would you expect the velocity to be at the pipe wall? For what r is u(r) equal to that?
 
The velocity should be 0 m/s at pipe wall right? Because of the no slip condition?
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
30,835
4,452

Want to reply to this thread?

"Fluid mechanics question" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top