2-For a certain incompressible flow field it is suggested that thevelocity components are given by the equationsu = 2xy v = –x²y w = 0Is this a physically possible flow field? Explain.

For an incompressible flow... The divergence of the velocity vector mustbe zero..

Answered: For a certain incompressible flow field…

For a certain incompressible flow field it is suggested tl 2- velocity components are given by the equations u = 2xy v = -xy w= 0 Is this a physically possible flow field? Explain.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.3P: Evaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK,...

See similar textbooks

Related questions

Q: Consider the flow with velocity field given as (F·x)x 1 F- 8TTur u ( with Ha given constant, F a…

A: Given : To find : Do fluid particles rotate

Q: Example 6.5. For a three-dimensional flow field described by V = (y² + 2?) i + (x² +2²) j + (x²+y?)…

Q: (d) Consider the following steady, three dimensional velocity field in Cartesian coordinates. V=…

A: The given velocity vector must satisfy equation of continuity. The condition is : a = 24c3

Q: two-dimensional flow field is given by o=Ux+ Klnr (a) Is this flow possible? (b)…

Q: Given the following steady, two-dimensional velocity field. [Diberi medan halaju yang mantap dan dua…

A: A flow is said to be incompressible if its density remains constant through out. An incompressible…

Q: Consider a flow field represented by the stream function ψ = (4+24) x3y - (6+24) x2y2 + (4+24) xy3.…

A: Given:Stream function ψ=(4+24) x3y - (6+24) x2y2 + (4+24) xy3⇒ψ=28 x3y -30) x2y2 + 28…

Q: Consider a steady, two-dimensional, incompressible velocity field with u = ax + b and ? = −ay + cx,…

Q: If a flow field is compressible, what can you say about the material derivative of density? What…

A: Concept: 1.If the density of fluid doesn't change, then the flow is incompressible. Example: Air…

Q: Consider a flow field represented by the stream function ψ=24 x3y - 26 x2y2 + 24 xy3. Is this a…

A: ψ=24x3y-26x2y2+24xy3a If stream function ψ satisfied laplace equation then flow is…

Q: Consider inviscid flow along the streamline approachingthe front stagnation point of a sphere, as in…

A: (a) It is known that along the stagnation streamline, the flow will be purely radial. Then, the…

Q: Consider a flow field represented by the stream function ψ = (4+2) x3y - (6+2) x2y2 + (4+2) xy3. Is…

A: It is a point as well as scalar function. It is defined for 2-D incompressible flow. It is defined…

Q: 8. Which of the following are required in order to use Bernoulli's equation? I. Steady flow, II)…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Consider a flow field represented by the stream functionψ=(4+1) x3y - (6+1) x2y2 + (4+1)xy3. Is this…

A: it is a point function. It is a scalar function. It is defined for 2-D incompressible flow. So, if…

Q: 6.15 mLEYe The stream function for an incompressible, two- dimensional flow field is 4 = ay – by…

Q: 2. A two-dimensional flow field for a inviscid, incompressible fluid is described by the velocity…

A: Given Data: The component of velocity in the x-direction is, u=U0+2y. The component of velocity in…

Q: Consider the following steady, two-dimensional, incompressible velocity field: V-› = (u, ? ) = (ax +…

A: The given velocity field is; V→=ui^+vj^=(ax+b)i^+(-ay+c)j^ The expression for the angular velocity…

Q: Given the following steady, two-dimensional velocity field. [Diberi medan halaju yang mantap dan dua…

Q: For a certain two-dimensional incompressible flow, velocity field is given by 2xy î - y?j. The…

Q: Consider a flow field represented by the stream function y = (4+6) x'y - (6+6) x²y² + (4+6) xy. Is…

A: Given data: The stream function is ψ=10x3y-12x2y2+10xy3

Q: c. Explain why the stream function ψ is restricted to 2-D flows and you have to use the velocity…

Q: Consider the following steady, two-dimensional, incompressible velocity field: V-› = (u, ? ) = (…

A: Given data u=12ay2+bv=axy2+c

Q: Q1 (a) If a flow field is compressible, what can you say about the material derivative of density?…

Q: Consider the steady, two-dimensional velocity field given by O = x2 – y? (i) (ii) Determine the…

Q: Consider the steady, two-dimensional velocity field given by V-› = (u, ?) = (1.6 + 2.8x) i-› + (1.5…

A: Given data: The two dimensional component, (u,v) = (1.6+2.8x)i + (1.5-2.8y)j. The condition for…

Q: In a steady, two-dimensional flow field in the xyplane, the x-component of velocity is…

A: Given data: The x- component of the velocity is, u = ax + by + cx2. As the flow is flow field is…

Q: consider flow field with purely tangential motion (circular streamlines) vr=0 and v0=f(r). Evaluate…

A: It is asked to prove the irrotational flow is function of 'r' to produce a free vortex

Q: Consider a steady velocity field given by V-› = (u, ?, w) = a(x2y + y2)i→ + bxy2 j→ + cxk→, where a,…

A: Given Data: The velocity field is V→=ax2y+y2i→+bxy2j→+cxk→ a, b and c are constants. The required…

Q: ing the continuity equation, what is the velocity component v in the y direction? Evaluate constant…

Q: 1. Consider a three-dimensional steady incompressible flow with components: u=-x(y+2), v= y²,…

A: u = -x(y+z)v = y2w = 12z2 -2yz

Q: Consider the steady, two-dimensional velocity field given by $ = x2 – y2 (i) (ii) Determine the…

Q: Two velocity components of a steady, incompressible flow field are known: u = 2ax + bxy + cy2 and…

A: Given u = 2ax+bxy+cy2 v = axz-byz2 assumptions The fluid flow is steady The flow is…

Q: 6.19 For a certain two-dimensional flow field u = 0 v = V (a) What are the corresponding radial and…

A: Given is For a 2 D flow field where u = 0 and v = V To determine (a) corresponding radial and…

Q: Consider the following steady, two-dimensional velocity field: V = (u, v) = (0.5 + 1.2x)i + (-2.0 –…

A: Given is V → = (0.5+1.2x)i + (-2.0-1.2y)j To find Location of the stagnation point

Q: The stream function for a two-dimensional incompressible flow field is y = - 2(x-y), what is the…

A: given; →stream function (ψ)=-(x-y)→velocity potential function(ϕ)=?

Q: 6.7 A one-dimensional flow is described by the velocity field u = ay + by² v = w = 0 where a and b…

Q: (b) Show that o = x #In(x? + y²) is a possible velocity potential for a two-dimensional…

Q: An Eulerian velocity field in Cartesian coordinates is given by u = x2y, v = −xy2,w = 2xy.…

A: given: An Eulerian velocity field in Cartesian coordinates is given by u = x2y, v = −xy2,w = 2xy.…

Q: If a flow field is compressible, what can you say about the material derivative of density? What…

A: Given:- Compressible flow field Incompressible flow field To find:- Material derivative of density

Q: A steady, two-dimensional velocity field is given byV-› = (u, ? )…

A: Given, The velocity field is, V→=u,v=2.85+1.26x-0.896yi→+3.45x+cx-1.26yj→ The flow is irrotational…

Q: 1 (a) If a flow field is compressible, what can you say about the material са derivative of density?…

Q: In a general flow field, the effect of viscosity would disappear when the Reynolds number (RN)…

Q: (a) If a flow field is compressible, what can you say about the material derivative of density? What…

A: Incompressible flow is defined as a flow in which the density fluctuation owing to pressure…

Q: During the course, we have learned about the Bernoulli equation as well as rotational and…

Q: (d) Consider the following steady, three dimensional velocity field in Cartesian coordinates. V =…

Q: For a two-dimensional incompressible flow field given by -Ajxi - vi , where A > 0, which one of the…

Q: A steady, three-dimensional velocity field is given byV-›= (0.657 + 1.73x + 0.948y + az) i-› + (2.61…

Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

2-
For a certain incompressible flow field it is suggested that the
velocity components are given by the equations
u = 2xy v = –x²y w = 0
Is this a physically possible flow field? Explain.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

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

(a) A two-dimensional flow field is given byu = 5x 2 − 5y 2v = −10xy(i) Find the streamfunction ψ and velocity potential φ.(ii) Find the equation for the streamline and potential line which passesthrough the point (1, 1).
1. The components of velocity in a flow field are given byu=x2+y2+z2v=xy+yz+z2w=-3xz- 0.5z2+4a) Determine the volumetric dilatation rate and interpret the result.b) Determine an expression for the rotation vector. Is this an irrotational flow field?
A steady, two-dimensional velocity field is given by V-›= (u, ? ) = (−0.781 − 3.25x) i-›+ (−3.54 + 3.25y) j-› Calculate the location of the stagnation point
For the flow field described by V = 2xyi − 3y2j. (a) Is the flow field incompressible? (b) Is the flow field steady? (c) Is the flow field two- or three-dimensional? (d) Find the angle the streamline makes that passes through the point (3, −2). (e) Find the acceleration of the flow field.
For the flow field described by u = 2, v = yz2t, w = −z3t/3. (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the z-component of the acceleration vector.
The velocity components of an incompressible, two-dimensional field are given bythe following equations: u(x,y) =y^2 -x (1+x) v(x,y) = y(2x+1) Show that the flow field is (a) irrotational and (b) satisfies conservation of mass.
Two velocity components of a steady, incompressible flow field are known: u = 2ax + bxy + cy2 and ? = axz − byz2, where a, b, and c are constants. Velocity component w is missing. Generate an expression for w as a function of x, y, and z.
The flow function for a flow field is given as ψ=x2*y-(y3/3).Find the speed potential. Provide detailed information about the current.
Consider a 2-dimensional incompressible flow field. The vertical component of velocity forthe flow field is given by 2y. The pressure at (x, y) = 0,0 is given by 3 bar absolute. The densityof the fluid is 1.2 Kg/m3 . Find. a) x-component of velocity; b) acceleration at point (x, y) = 2,1;c) pressure gradient at the same point; d) pressure gradient along the x-axis; e) check whetherthe flow is irrotational; f) find the potential function; g) find the stream function; h) equationfor streamline and sketch few streamlines.
For the velocity field that is linear in both spatial directions (x and y) is V-›= (u, ? ) = (U + a1x + b1y) i-›+ (V + a2x + b2y) j-›where U and V and the coefficients are constants, calculate the linear strain rates in the x- and y-directions
The stream function of an unsteady two-dimensional flow field is given by ? = (4x/y2 )t Sketch a few streamlines for the given flow on the xy-plane, and derive expressions for the velocity components u(x, y, t) and v(x, y, t). Also determine the pathlines at t = 0.
1. For a velocity field described by V = 2x2i − zyk, is the flow two- or threedimensional? Incompressible? 2. For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0, find the slope of the streamline passing through the point [2, 4] at t = 2. 3. Find the angle the streamline makes with the x-axis at the point [-1, 0.5] for the velocity field described by V = −xyi + 2y2j