Q.5A stream function is given by Y = (x² – y2).The Velocity potential function (b) of theflow will beA 2xy + f(x)B -2xy + constant© 2(x2 -y2)D 2xy + f(y)

Answered: A stream function is given by y = (x:…

Engineering

Mechanical Engineering

A stream function is given by y = (x: %3D The Velocity potential function () o

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

Related questions

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

Q: 1. For a certain incompressible two-dimensional flow, the stream function, ψ(x, y) is…

A: For incompressible flow, the partial derivative of the stream function with one of the dependent…

Q: Consider a line vortex, defined as steady, planar, incompressible flow in which the velocity…

A: Write the given information: Line vortex flow which is steady, planar and incompressible.

Q: For the flow field given in Cartesian coordinates by u = 0, v = x2z, w = z3: (a) Is the flow…

A: For flow to be compressible it must satisfy the below equation. Therefore its compressible flow…

Q: Imagine a steady, two-dimensional, incompressible flow that is purely circular in the xy- or…

A: Write the expression of the continuity equation in 2-D polar co-ordinates. Since the flow is…

Q: Consider a uniform stream of magnitude V inclined at angle ?. Assuming incompressible planar…

A: The components of velocity in x and y-directions are given in the diagram, It is written as, For…

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: QI\ If stream function for steady flow is given by y = 2xy – 4x? – 4y2, 1)determine whether the flow…

Q: Converging duct flow is modeled by the steady, twodimensional velocity field V-›= (u, ? ) = (U0 +…

A: We have to use the equation for volumetric strain rate to verify that his flow feild is…

Q: When a line source–sink pair with m= 2 m2/s is combinedwith a uniform stream, it forms a Rankine…

A: Given Mass flow rate = 2 m2/s Oval dimension = 40 cm = 0.4m To find Stream velocity Velocity of the…

Q: QI A/ The inviscid, steady, and incompressible 2D flows are given by (a) o = x-3xy (b) y =x- 2xy-y?…

A: Velocity potential functionφ is defined as a scalar function of space and time such that its…

Q: Consider a velocity field where the x and y components of velocity aregiven by u = cy/(x2 + y2) and…

A: Given Data: The x- component of velocity is u = cy/(x2+y2). The y-component of velocity is v =…

Q: "Streamline is a strictly Eulerian concept and pathline is a strictly Lagrangian concept"- ify this…

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

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

Q: Show that the axisymmetric potential flow formed by the superpositionof a point source +m at (x, y)…

A: The velocity of flow can be expressed as, Here, u: velocity of flow towards the body of revolution…

Q: Using cartesian coordinates, show that each velocity component(u, υ, w) of a potential flow…

A: Given Data: The velocity component is given as u,v,w. Let the potential function ϕ be, ϕ=fx,y,z,t…

Q: Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23…

A: The shape of streamlines will change with the direction of resultant velocity changes. For…

Q: Consider the flow represented by the stream function p = 2x²y – 3y. What are the velocity…

A: The stream function of the flow is given as, Ψ=2x2y-3y3

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

A: Given data: The steady incompressible two-dimensional velocity field is; V→=u,v=ax+bi→+-ay+cj→.…

Q: Find the stream function associated with the two-dimensional incompressible, possible flow with…

A: For cylindrical coordinates, Stream function ψ can be found using below relations: (1) ur = 1r ∂ψ∂θ…

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

A: The given velocity field is: At stagnation point, the velocity of fluid must be zero. Therefore,

Q: derive equation of stream line in 2 dimensions

Q: consider the 2 dimensional velocity field V= -Ayi +Axj where in this flow field does the speed…

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: Find the stream function associated with the two-dimensional incompressible, possible flow with…

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: An incompressible, irrotational, two-dimensional fl ow hasthe following stream function in polar…

Q: For the flow field given in Cartesian coordinates by u = 2xt + y, v = −2yt, w = 0: (a) Is the…

A: Given Data Velocity in x direction, u = 2xt + y, Velocity in y direction, v = −2yt, Velocity in z…

Q: The u velocity component of a steady, two-dimensional, incompressible flow field is u = 3ax2 − 2bxy,…

A: For 2 Dimensional incompressible flow dudx+dvdy=0 dudx=-dvdy ...............(1) Given value u =…

Q: An incompressible stream function is given byψ = aθ +br sin θ. ( a ) Does this flow have a…

A: (a) The radial component of the velocity function is written as,…

Q: The equation of streamlines is:

Q: Consider the two-dimensional incompressible velocity potentialϕ = xy + x 2 - y 2 . ( a ) Is it true…

Q: V = uî + vỹ + wk [m/s] u = 3xy? v = 10z?y w = 5

A: stress tensor is defined by general expression as given in below image. find all the term and put…

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: Theodore von Kármán in 1930 theorized that turbulentshear could be represented by τturb = ε du/dy,…

A: As we know that turbulence shear stress at the wall is equal to the wall shear stress. τturb=τw…

Q: Consider the following steady, incompressible, two-dimensional velocity field: V = (u, v) = x²i +…

A: Given Data: It is a steady ,incompressible and two dimensional velocity field.

Q: QUESTION 3. Velocity components of a two dimensional fluid flow are: u = 2xy + t° and v =x²-y² +…

A: Hi, you have submitted multiple subpart questions and it is not specified which parts you need help…

Q: The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, µ)…

A: The boundary conditions for the given pattern of the bearing lubrication can be determined from its…

Q: For the velocity field in u = Ax , υ = By , and w = Cxy , the convectiveacceleration in the…

A: To find out the convective acceleration in the x-direction ax=ududx+vdudy+dudt

Q: For each statement, choose whether the statement is true or false, and discuss your answer briefly.…

A: (a) For the velocity potential function u=-d∅dxv=-d∅dyw=-d∅dz The negative direction indicate the…

Q: Investigate the velocity potential ϕ = Kxy , K = constant.Sketch the potential lines in the full xy…

A: The potential lines are represented as, ϕ = Kxy , K = constant. Hence the potential lines are…

Q: A steady, two-dimensional, incompressible flow field in the xy-plane has a stream function given by…

A: ψ=ax2 + by2 + cydψdy=u v=-dψdx

Q: Find the stream function associated with the two-dimensional incompressible, possible flow with…

Q: H.W : a stream function is given by : Y = 2x?y + (x+t)y Find the velocity equation for fluid at time…

Q: what are velocity components,potential function and stream function?…

A: Stream Function→ for 2D flow and 3D axial symmetric flows stream functions are defined. stream…

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

100%

Q.5
A stream function is given by Y = (x² – y2).
The Velocity potential function (b) of the
flow will be
A 2xy + f(x)
B -2xy + constant
© 2(x2 -y2)
D 2xy + f(y)

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

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

Problem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.
4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk , V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?
1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.
Assumptions The flow is steady. The flow is incompressible. The flow is two-dimensional in the x-y plane V = (u, v) = (U, + bx) ỉ - byj %3D We are to calculate the material acceleration for a given velocity field. (None = b( U, +bx) a. y b? y = b( U, +by) ax b2 x (Uo +bx) = b y a, II
QI A/ The inviscid, steady, and incompressible 2D flows are given by (a) o =x- 3xy (b) y = x-2xy-y? In each case, find the components of velocity in x- and y-directions.
A two dimensional, steady, incompressible and potential flow field of water (ρ=1000 kg/m3) is given with velocity components u and v. If the velocity component, u is given as u=2xy m/s with the magnitude of maximum pressure in the field as 52108 Pa. a) At x=+1 m and y=+2 m point, what is the magnitude of the velocity component v (in m/s)? (Please use 2 decimal digits in your answer) b) At x=+1 m and y=+2 m point, what is the magnitude of dynamic pressure (in Pa)? (Please do not use any decimal digit in your answer) c) At x=+1 m and y=+2 m point, what is the magnitude of static pressure (in Pa)? (Please do not use any decimal digit in your answer)
Q4: The velocity components for a two dimensional incompressible flow are - 6xy, v = -3x² + 3y2 1) Is the flow satisfied the continuity equation?. u = 2) Obtain an expression of stream function 3) Obtain an expression for the velocity potential if it is exsits.
3.4 Consider a steady, incompressible, 2D velocity field for motion parallel to the X-axis with constant shear. The shear rate is du/dy Ay. Obtain an expression for the velocity field V. Calculate the rate of rotation. Evaluate the stream function %3D for this flow field. Ay Ay + В і, о, Ay + By+ C 6. Ans: V= 2
6. Problem We want to know the velocity component of a fluid flow normal to a given surface: v, = v"n. Compute the normal velocity u, for the following normal vector and flow vector. ) --E- 3.0 v = m/s V3 1.0
The velocity potential function (0) is given by an expression xy' x'y x* + 3 3 (i) Find the velocity components in x and y direction. (ii) Show that o represents a possible case of flow.
Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 s
Q4: The velocity components for a two dimensional incompressible flow are u = - 6xy, v=-3x2 + 3y2 1) Is the flow satisfied the continuity equation?. 2) Obtain an expression of stream function 3) Obtain an expression for the velocity potential if it is exsits.