Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
Pressure Flow, Flat Plates. Adverse pressure gradients in flow over bodies lead to flow reversal & separation, wakes, and increased drag. To examine such behavior, consider fully developed, laminar flow between two flat pates a distance & apart. The bottom plate is fixed, and the top plate moves with speed U (representing the outer flow over a boundary layer of thickness 8). (a) Derive the critical adverse pressure gradient, (dp/dx)*, above which there will be flow reversal, by solving the N-S equation in the coordinates shown, to get a relation for u(y), du/dy, and the critical (dp/dx)* in terms of 8, U, and μ above which there will be flow reversal at the lower plate. (b) If 8 = 5 mm and U = 10 m/s, evaluate (dp/dx)* if the fluid is air.

Pressure Flow, Flat Plates. Adverse pressure gradients in flow over bodies lead to flow reversal & separation, wakes, and increased drag. To examine such behavior, consider fully developed, laminar flow between two flat pates a distance & apart. The bottom plate is fixed, and the top plate moves with speed U (representing the outer flow over a boundary layer of thickness 8). (a) Derive the critical adverse pressure gradient, (dp/dx)*, above which there will be flow reversal, by solving the N-S equation in the coordinates shown, to get a relation for u(y), du/dy, and the critical (dp/dx)* in terms of 8, U, and μ above which there will be flow reversal at the lower plate. (b) If 8 = 5 mm and U = 10 m/s, evaluate (dp/dx)* if the fluid is air.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
See similar textbooks
icon
Related questions
Question

Assume Patm = 10^5, Pa = 14.7 psi ; ρwater ~ 1000 kg/m3 ; ρair ~ 1.2 kg/m3 ; μwater ~ 10^-3 N•s/m2 ; μair ~ 2 x 10^-5 N•s/m2 ; Vwater ~ 10^-6 m2 /s ; Vair ~ 1.67 x 10^-5 m2 /s ; g = 9.8 m/s^2 .; 1 m/s = 2.24 mph ; 1lbf = 4.45 N ; 1 m^3 = 264 gallons

note : get reversal when du/dy <0 at y = 0

**Pressure Flow, Flat Plates.** Adverse pressure gradients in flow over bodies lead to flow reversal and separation, wakes, and increased drag. To examine such behavior, consider fully developed, laminar flow between two flat plates a distance δ apart. The bottom plate is fixed, and the top plate moves with speed U (representing the outer flow over a boundary layer of thickness δ). (a) Derive the critical adverse pressure gradient, \((dp/dx)^*\), above which there will be flow reversal, by solving the Navier-Stokes equation in the coordinates shown, to get a relation for \(u(y)\), \(du/dy\), and the critical \((dp/dx)^*\) in terms of δ, U, and μ above which there will be flow reversal at the lower plate. (b) If δ = 5 mm and U = 10 m/s, evaluate \((dp/dx)^*\) if the fluid is air.
Transcribed Image Text:**Pressure Flow, Flat Plates.** Adverse pressure gradients in flow over bodies lead to flow reversal and separation, wakes, and increased drag. To examine such behavior, consider fully developed, laminar flow between two flat plates a distance δ apart. The bottom plate is fixed, and the top plate moves with speed U (representing the outer flow over a boundary layer of thickness δ). (a) Derive the critical adverse pressure gradient, \((dp/dx)^*\), above which there will be flow reversal, by solving the Navier-Stokes equation in the coordinates shown, to get a relation for \(u(y)\), \(du/dy\), and the critical \((dp/dx)^*\) in terms of δ, U, and μ above which there will be flow reversal at the lower plate. (b) If δ = 5 mm and U = 10 m/s, evaluate \((dp/dx)^*\) if the fluid is air.
**Ans OM:** (a) \( u(y) \sim A(y/\delta) + B(y/\delta)^2 \) \( (dp/dx)^* \sim C(\mu U/\delta^2) \) (b) \( (dp/dx)^*: 10^1 \, \text{Pa/m} \)
Transcribed Image Text:**Ans OM:** (a) \( u(y) \sim A(y/\delta) + B(y/\delta)^2 \) \( (dp/dx)^* \sim C(\mu U/\delta^2) \) (b) \( (dp/dx)^*: 10^1 \, \text{Pa/m} \)
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Compressible Flow
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS