Connect Access for Fluid Mechanics
4th Edition
ISBN: 9781259877759
Author: Yunus A. Cengel Dr.
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 10, Problem 1CP
Discuss how nondimensalizsionalization of the Navier-Stokes equation is helpful in obtaining approximate solutions. Give an example.
Expert Solution & Answer
To determine
The advantages of solving Navier Strokes equation using non-dimensionalization.
Explanation of Solution
Non-dimensionalization of Navier-Stokes equation helps in obtaining approximate solutions. This can be explained from below mentioned points:
- Non-dimensionalization helps in reducing the complexity of any equation.
- It helps in removing the dimensions of the all the quantities present.
- The primary function is to make the dimension of the quantities present in Navier-Stokes equation unity.
- It calculates small quantities with respect to a large quantity.
- For example- If the value of Strouhal number is less with respect to Reynolds number, we can ignore the term containing Strouhal number whereas the respective value of Reynolds number must retain.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Simplify the Navier-Stokes equations, explaining any assumptions you make.
Write a one-word description of each of the five terms in the incompressible Navier–Stokes equation, When the creeping flow approximation is made, only two of the five terms remain. Which two terms remain, and why is this significant?
Write out the three components of the Navier–Stokes equation in Cartesian coordinates in terms of modified pressure. Insert the definition of modified pressure and show that the x-, y-, and z-components are identical to those in terms of regular pressure. What is the advantage of using modified pressure?
Chapter 10 Solutions
Connect Access for Fluid Mechanics
Ch. 10 - Discuss how nondimensalizsionalization of the...Ch. 10 - Prob. 2CPCh. 10 - Expalain the difference between an “exact”...Ch. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - A box fan sits on the floor of a very large room...Ch. 10 - Prob. 9PCh. 10 - Prob. 10P
Ch. 10 - Prob. 11PCh. 10 - In Example 9-18 we solved the Navier-Stekes...Ch. 10 - Prob. 13PCh. 10 - A flow field is simulated by a computational fluid...Ch. 10 - In Chap. 9(Example 9-15), we generated an “exact”...Ch. 10 - Prob. 16CPCh. 10 - Prob. 17CPCh. 10 - A person drops 3 aluminum balls of diameters 2 mm,...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Consider again the slipper-pad bearing of Prob....Ch. 10 - Consider again the slipper the slipper-pad bearing...Ch. 10 - Prob. 30PCh. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - Prob. 34EPCh. 10 - Discuss what happens when oil temperature...Ch. 10 - Prob. 36PCh. 10 - Prob. 38PCh. 10 - Prob. 39CPCh. 10 - Prob. 40CPCh. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Prob. 47PCh. 10 - Prob. 48PCh. 10 -
Ch. 10 - Prob. 50CPCh. 10 - Consider the flow field produced by a hair dayer...Ch. 10 - In an irrotational region of flow, the velocity...Ch. 10 -
Ch. 10 - Prob. 54CPCh. 10 - Prob. 55PCh. 10 - Prob. 56PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 58PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 60PCh. 10 - Consider a steady, two-dimensional,...Ch. 10 -
Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - In an irrotational region of flow, we wtite the...Ch. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Water at atmospheric pressure and temperature...Ch. 10 - The stream function for steady, incompressible,...Ch. 10 -
Ch. 10 - We usually think of boundary layers as occurring...Ch. 10 - Prob. 73CPCh. 10 - Prob. 74CPCh. 10 - Prob. 75CPCh. 10 - Prob. 76CPCh. 10 - Prob. 77CPCh. 10 - Prob. 78CPCh. 10 - Prob. 79CPCh. 10 - Prob. 80CPCh. 10 - Prob. 81CPCh. 10 -
Ch. 10 - On a hot day (T=30C) , a truck moves along the...Ch. 10 - A boat moves through water (T=40F) .18.0 mi/h. A...Ch. 10 - Air flows parallel to a speed limit sign along the...Ch. 10 - Air flows through the test section of a small wind...Ch. 10 - Prob. 87EPCh. 10 - Consider the Blasius solution for a laminar flat...Ch. 10 - Prob. 89PCh. 10 - A laminar flow wind tunnel has a test is 30cm in...Ch. 10 - Repeat the calculation of Prob. 10-90, except for...Ch. 10 - Prob. 92PCh. 10 - Prob. 93EPCh. 10 - Prob. 94EPCh. 10 - In order to avoid boundary laver interference,...Ch. 10 - The stramwise velocity component of steady,...Ch. 10 - For the linear approximation of Prob. 10-97, use...Ch. 10 - Prob. 99PCh. 10 - One dimension of a rectangular fiat place is twice...Ch. 10 - Prob. 101PCh. 10 - Prob. 102PCh. 10 - Prob. 103PCh. 10 - Static pressure P is measured at two locations...Ch. 10 - Prob. 105PCh. 10 - For each statement, choose whether the statement...Ch. 10 - Prob. 107PCh. 10 - Calculate the nine components of the viscous...Ch. 10 - In this chapter, we discuss the line vortex (Fig....Ch. 10 - Calculate the nine components of the viscous...Ch. 10 - Prob. 111PCh. 10 - The streamwise velocity component of a steady...Ch. 10 - For the sine wave approximation of Prob. 10-112,...Ch. 10 - Prob. 115PCh. 10 - Suppose the vertical pipe of prob. 10-115 is now...Ch. 10 - Which choice is not a scaling parameter used to o...Ch. 10 - Prob. 118PCh. 10 - Which dimensionless parameter does not appear m...Ch. 10 - Prob. 120PCh. 10 - Prob. 121PCh. 10 - Prob. 122PCh. 10 - Prob. 123PCh. 10 - Prob. 124PCh. 10 - Prob. 125PCh. 10 - Prob. 126PCh. 10 - Prob. 127PCh. 10 - Prob. 128PCh. 10 - Prob. 129PCh. 10 - Prob. 130PCh. 10 - Prob. 131PCh. 10 - Prob. 132PCh. 10 - Prob. 133PCh. 10 - Prob. 134PCh. 10 - Prob. 135PCh. 10 - Prob. 136PCh. 10 - Prob. 137PCh. 10 - Prob. 138P
Knowledge Booster
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.Similar questions
- Discuss how nondimensionalization of the Navier– Stokes equation is helpful in obtaining approximate solutions. Give an example.arrow_forwardSimplify the Navier–Stokes equation as much as possible for the case of incompressible hydrostatics, with gravity acting in the negative z-direction. Begin with the incompressible vector form of the Navier–Stokes equation, explain how and why some terms can be simplified, and give your final result as a vector equation.arrow_forwardDerive the Navier stokes equation in detail.If you copy from other source I will give you thumbs down.arrow_forward
- In this chapter, we make a statement that the boundary layer approximation “bridges the gap” between the Euler equation and the Navier–Stokes equation. Explainarrow_forwardQ2:: Discuss the usefulness of Navier-Stokes equation with the help of practical examples.arrow_forwardWhich nondimensional parameter in the nondimensionalized Navier–Stokes equation is eliminated by use of modified pressure instead of actual pressure? Explain.arrow_forward
- What is the most significant danger associated with an approximate solution of the Navier–Stokes equation? Give an example that is different than the ones given in this chapter.arrow_forwardHow do I solve these questions?: a) Start with Navier-Stokes equations and determine the velocity at the point x = 4 cm and y= 0.58 cm. The value of the velocity is ________ b) Calculate the magnitude of the vorticity at the same point. The magnitude value of vorticity is ________ c) Calculate the rate of angular deformation at the same point. The angular deformation value is ________arrow_forwardThe velocity components are ur = 0, u? = Г/(2?r), and uz = 0. Compute the viscous term of the ?-component of the Navier–Stokes equation, and discuss. Verify that this velocity field is indeed irrotational by computing the z-component of vorticity.arrow_forward
- Which equation is the proper approximate Navier– Stokes equation in dimensional form for creeping flow? (a) ∇-›P − ρg-›= 0 (b) −∇-›P + ?∇-›2V-›= 0 (c) −∇-›P + ρg-›+ ?∇-›2V-›= 0 (d ) ρ(DV-›/Dt) = −∇-›P + ρg-›+ ?∇-›2V-› (e) ρ(DV-›/ Dt) +∇-›P − ρg-›= 0arrow_forwardWhat is the most important criterion for use of the modified pressure P′ rather than the thermodynamic pressure P in a solution of the Navier–Stokes equation?arrow_forwardHow does the Navier-Stokes equation encapsulate the complexities of fluid behavior, and what challenges arise when attempting to solve it in the context of mechanical engineering's fluid mechanicsarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Physics 33 - Fluid Statics (1 of 10) Pressure in a Fluid; Author: Michel van Biezen;https://www.youtube.com/watch?v=mzjlAla3H1Q;License: Standard YouTube License, CC-BY