Question

25 Air at 25°C flows over a flat plate with a velocity of 2 m/s. Using Blasius' exact solution, find: a) The Reynolds number and boundary layer thickness at 20 mm from the leading edge and also at the end of the laminar boundary layer. b) The rate of growth of the boundary layer at the two points in (a) above. The thickness δ/x = 5.48/√(VRe_x), the displacement thickness δ/x = 1.828/√(VRe_x), and the B.L momentum thickness θ/x = 0.731/√(VRe_x), and the skin friction coefficient cf/x = 0.731/√(VRe_x). Repeat the same calculations using a 3rd order velocity profile. Compare the results with those obtained using Blasius' exact solution. Comment on the accuracy of the results in all three solutions.

          25 Air at 25°C flows over a flat plate with a velocity of 2 m/s. Using Blasius' exact solution, find: 
    a) The Reynolds number and boundary layer thickness at 20 mm from the leading edge and also at the end of the laminar boundary layer.
    b) The rate of growth of the boundary layer at the two points in (a) above.
    
    The thickness δ/x = 5.48/√(VRe_x), the displacement thickness δ/x = 1.828/√(VRe_x), and the B.L momentum thickness θ/x = 0.731/√(VRe_x), and the skin friction coefficient cf/x = 0.731/√(VRe_x). 
    Repeat the same calculations using a 3rd order velocity profile. Compare the results with those obtained using Blasius' exact solution. Comment on the accuracy of the results in all three solutions.
        
Show more…
25 air at 25c flows over a flat plate with a velocity of 2 msusing blasius exact solution find a the reynolds number and boundary layer thickness at 20 mm from the leading edge and also at t 48808

Added by Michael G.

Close

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
25 Air at 25°C flows over a flat plate with a velocity of 2 m/s. Using Blasius' exact solution, find: a) The Reynolds number and boundary layer thickness at 20 mm from the leading edge and also at the end of the laminar boundary layer. b) The rate of growth of the boundary layer at the two points in (a) above. The thickness δ/x = 5.48/√(VRe_x), the displacement thickness δ/x = 1.828/√(VRe_x), and the B.L momentum thickness θ/x = 0.731/√(VRe_x), and the skin friction coefficient cf/x = 0.731/√(VRe_x). Repeat the same calculations using a 3rd order velocity profile. Compare the results with those obtained using Blasius' exact solution. Comment on the accuracy of the results in all three solutions.
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn Ivan Kochetkov
David Collins verified

Adi S and 57 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
only-full-solution-please-lthe-velocity-distribution-of-a-given-laminar-boundary-layer-is-u-u-is-the-boundary-layer-thickness-derivethe-value-of-k8and-8-2the-velocity-distribution-of-laminar-21727

The velocity distribution of a given laminar boundary layer is: u/U = 1 - e^(-k y/ͅ). ͅ is the boundary layer thickness. Derive: The value of k, ͅ*/ͅ and ̑/ͅ. 2. The velocity distribution of laminar boundary layer on a flat plate is: u/U = 2y/ͅ - (y/ͅ)^2. ͅ is the boundary layer thickness. Derive: displacement thickness ͅ* and momentum thickness ̑. 3. The air flows through a flat plate with the velocity of 30m/s. The temperature of air is 25°C. The length of the plate is 500mm. Derive: (1) The boundary layer thickness, displacement thickness and momentum thickness at the position of 200mm from the leading edge of the plate. (2) The friction coefficient of the plate.

Adi S.

a-laminar-boundary-layer-develops-on-a-flat-plate-immersed-in-an-airstream-with-u-5-ms-and-a-temperature-t-20-c-fix-your-attention-on-a-station-x-025-m-downstream-of-the-leading-edge-a-what-19619

Adi S.

numerical-results-of-the-blasius-solution-to-the-prandtl-boundary-layer-equations-are-presented-in-t

Numerical results of the Blasius solution to the Prandtl boundary-layer equations are presented in Table $9.1 .$ Consider steady, incompressible flow of standard air over a flat plate at freestream speed $U=5 \mathrm{m} / \mathrm{s}$. At $x=20 \mathrm{cm},$ estimate the distance from the surface at which $u=0.95 U$. Evaluate the slope of the streamline through this point. Obtain an algebraic expression for the local skin friction, $\tau_{w}(x)$. Obtain an algebraic expression for the total skin friction drag force on the plate. Evaluate the momentum thickness at $L=1 \mathrm{m}$.

Introduction to Fluid Mechanics


*

Recommended Textbooks

-
University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young 14th Edition
achievement 1,702 solutions
Physics: Principles with Applications

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition
achievement 1,513 solutions
Fundamentals of Physics

Fundamentals of Physics

David Halliday, Robert Resnick , Jearl Walker 10th Edition
achievement 1,674 solutions

*

Transcript

-
00:02 Of a given liminary boundary is u equal to u 1 minus k x upon boundary layer thickness ok.
00:17 So, u represent the velocity of the fluid at the distance x from the hole and the capital u is the free stream velocity ok, k is the constant and this symbol is the boundary layer thickness.
00:36 So, the value of k can be determined by setting u equal to 0 at x equal to boundary layer ok.
00:45 So, this is the equation theta equal to u 1 minus k boundary thickness upon boundary thickness ok.
00:55 So, solving for k we get k equal to 1 ok.
01:01 So, the value of value of thickness boundary thickness upon boundary thickness can be determined by using the setting u equal to u by 2 at x equal to boundary thickness...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever