B. a. An incompressible, inviscid fluid flows steadily past a ball of radius R, as shown in the figure below. According to a more advanced analysis of the flow, the fluid velocity along streamline A-B is given by R3 V = u(x)i = v (1+ i

B. a. An incompressible, inviscid fluid flows steadily past a ball of radius R, as shown in the figure below. According to a more advanced analysis of the flow, the fluid velocity along streamline A-B is given by R3 V = u(x)i = v (1+ i

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: (b) Two velocity components of a steady, incompressible flow field are given as follows; и 3 2ах +…

Q: d flow is represented by the velocity = 2xi + 4yj . The equation of stream line paSSI gh a point (2,…

Q: A two-dimensional flow field is given by the equations: u = ax + by V = Cx + dy Give one possible…

A: Given, u = ax + byv = cx + dy We can use continuity equation for incompressible flow in order to…

Q: 3.4 The stream function in a two dimensional flow field is given by y = x² - y? The magnitude of the…

Q: 3. The two-dimensional velocity field v = (3t- 8xy)i+ 4(y – x')j satisfies the Euler's equation of…

Q: Question 3: Air through a Jet Engine: A streamline that goes through a jet engine is shown in the…

Q: Q3/ Prove that in a two dimensional fluid flow, the stream function: -xy is harmonic. = zk+zx

A: Given dataStream function φ=-xyx2+y2To prove the given stream function is harmonic in two…

Q: Show that the incompressible velocity potential in plane polar coordinates o(r, 0) is such that аф 1…

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

Q: The velocity field of an incompressible flow is given by V = (a,x + a,y + azZ)i + (b,x + b,y + b3z)j…

A: Answer: The value of b2 is 2.

Q: 1. Consider the steady, two-dimensional, frictionless velocity V= (u,v) = (ax +b)i+(-ay+cx)j . 1) Is…

Q: The velocity components in x and y direction are given by u = Axy3 - x²y; v = xy² – 3/4 ху y4. The…

A: Given:u=λxy3-x2yv=xy2-34y4

Q: If stream function Y = 2xy, then the velocity at a point (1, 2) is equal to (а) 2 (c) /20 (b) 4 (d)…

A: Given, Stream function = ψ = 2xy x component of velocity is given by, u = ∂ψ∂y= ∂∂y (2xy)= 2x y…

Q: Prove that the change in Y is zero along a streamline,

A: Given: Stream function along stream line TO prove: Stream function along stream line is consatnt

Q: Define rotational and irrotational flow. The stream function and velocity potential for a flow are…

Q: The velocity field of an incompressible flow is given by V = (a1x + a2y + a3z)i + (b1a + b2y + bzz)j…

A: Given, V = ( a1x + a2y + a3z ) i + ( b1x + b2y + b3z ) j + ( c1x + c2y + c3z ) k a1 = 2 c3 = -4…

Q: The velocity components for a three dimensional incornpressible flow is given by : u=x'-y-2x,…

Q: Consider the velocity field f= 2xi - y} A) Get an equation for flow lines. B)Draw a flow line…

A: Velocity components of fluid in x and y directions: u=2x v=-y

Q: 4. Show that v = 3xi+ (t- 6xy)j is a possible fluid velocity fo unsteady flow of a homogeneous…

A: GivenV=3x2i+t-6xyjandF=6yti+18x2yj

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: A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V…

A: V=-2xyi+y2-x2ju=-2xy v=y2-x2

Q: 1. If u = 3x*yt and v = -6x°y´t" answer the following questions giving reasons, Is this flow or…

A: In Eulerian approach of study of fluid particles certain region in space is taken as observable…

Q: 1. If u 3x*yt and v- -6x'y*t° answer the following questions giving reasons, Is this flow or fluid:…

A: a. if the flow satisfy the continuity equation then it said to be possible flow ∂u∂x+∂v∂y=0…

Q: V = axi + ayj, where a is a constant. The equation %3D of stream line passing through a point (1, 2)…

A: Given data; A fluid flow is represented by the velocity field which is given as;…

Q: The stream function for a particular flow is given by the equation: w = 2x² – 2y? Determine the…

A: Write the given stream function. ψ=2x2-2y2 Here, ψ is the stream function, x is the x-coordinate of…

Q: The velocity field of a flow is given by V= axyi + by^2j where a = 1 m^-1s^-1 and b = - 0.5…

A: For the given velocity flow field V = axy i + by2 j where a = 1 m-1s-1 b = - 0.5 m-1s-1 To…

Q: A two-dimensional incompressible flow field is defined by the velocity components u= 2V(플 - v = -2v2…

A: Given Data: The x-component of velocity is u=2VxL-yL The y-component of velocity is v=-2VyL Let…

Q: The velocity components of an incompressible, two- dimensional velocity field are given by the…

Q: Consider the steady, two-dimensional velocity field given by V=(1.3+2.8x)/+(1.5-2.8y)/ Determine;…

A: Determine: (i) the fluid speed at origin; (ii) the location of stagnation point in the flow; and…

Q: The flow of an incompressible §uid is defined by u=3, v=9x. Does a stream function exist for this…

A: Write the given data with suitable variables. u=3v=9x

Q: 3. The velocity components in a two dimensional flow field for an incompressible fluid are expressed…

A: Solution(a) Velocity component in a two dimensional flowfor an incompressible…

Q: Question 4. The stream function is given as w=x³-y³. a. Is this flow possible? b. Is the flow…

Q: 6. Consider the steady, two-dimensional velocity field given by V = (1.3 + 2.8x)i+(1.5 – 2.8y)j.…

Q: Does the velocity potential exist for two dimensional incompressible flow prescribed by u = x-4y; v…

A: Given:u=x-4yv=-y-4x

Q: Q1 For a certain incompresible flow field, it is suggested that the velocity components are given by…

Q: Establish the equation of continuity for an incompressible fluid in the form V.V = 0 , V(u, v, w)…

Q: If stream function for steady flow is given by y = (y* – x*), determine whether the flow is…

Q: Determine whether each of the followings are rotational flow or irrotational flow. Also, determine…

Q: 1. If u = 3x*yt and v = -6x°y´t´ answer the following questions giving reasons, Is this flow or…

A: The velocities along x and y axis are given as a function of space and time. Given problem belongs…

Q: (b) Two velocity components of a steady, incompressible flow field are given as follows; u = 2ax +…

Q: Find the two-dimensional velocity potential ϕ ( r , θ ) for thepolar coordinate fl ow pattern υ r =…

A: Write the relation between polar coordinate and radial velocity flow patterns.

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

A: Given: The flow velocity in x-direction is u=cy/(x2+y2). The flow velocity in y-direction is v=-…

Q: Sources of equal strength m are placed at the four symmetricpositions (x, y) = (a, a), (-a, a), (-a,…

A: Source have equal strength are placed at symmetric position (x,y)=a,a, -a,a, -a,-a, and a,-a. The…

Q: 6.4 The three components of velocity in a flow field are given by u = x² + v² + z² v = xy + yz + z?…

Q: Q.1 b) 1. Find the velocity at a point (4, 3, 1) after 2 sec. for a three dimensional flow given by…

A: In a flow field, the fluid moves in such a way that the mass is always conserved. This is known as…

Q: Consider the flow along a streamline below. The velocity along streamline is given by V=(0. 4 S2 )…

Q: Question 3 Consider the two-dimensional incompressible velocity potential O = xy + x? – y² a) Show…

Q: II ) The complex potential is w(z) = mln z - in which m is a given real constant, (1) What kinds of…

Q: Two velocity components of a steady, incompressible flow field are given as follows; u = 2ax + bxy +…

Q: The stream function o in a two-dimensional flow field is given as p = 4x – 3y + 7xy (a) Prove that…

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

3. a. An incompressible, inviscid fluid flows steadily past a ball of radius
R, as shown in the figure below.
According to a more advanced analysis of the flow, the fluid velocity
along streamline A-B is given by
R3
V = u(x)i = v. 1+
x3
where V is the upstream velocity far ahead of the sphere. Determine
the acceleration experienced by fluid particles as they flow along this
streamline.

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

Study of velocity

VIEW

acceleration

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

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

5- The x and y components of velocity for 2D flow are u=6y ft/s, and ??=3 ft/s, where y in feel. Determine the equation of streamline
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.
θ(x,y)=x2-y2+2xy According to the potential equation of a two-dimensional flow in the horizontal plane defined as;1-) Is this current physically possible?2-) Determine the current function?3 -) Calculate the resultant velocity and resultant acceleration at the point (5,6).4 -) Calculate the flow rate passing between (2,2) and (3,3) streamlines.
) The stream function for an incompressible flow field is given by the equation ψ=3x2y+y3 where the stream function has the units of with x and y in meters. (a) Sketch the streamline passing through the origin. (b) Determine the rate of flow across the straight path.
According to the potential equation of a two-dimensional flow in the horizontal plane defined as; i-) Is this current physically possible? Prove ii-) Determine the current function ψ (x, y) of this current. [ψ (0,0) = 0] iii-) Calculate the resultant velocity and resultant acceleration at point A (e, f) in this flow field. iv-) Calculate the flow rate passing between the streamlines ψ (a, a) and ψ (c, c).
It is given as u = 2 (1 + t), v = 3 (1 + t), w = 4 (1 + t) in a flow field. Accordingly, find the velocity and acceleration values at the points (3,2,4) at t=2 seconds.
Determine the third velocity component v such that all the components satisfy the continuityequation. The two components are as follows:u = 2xt– 3xyz + 4xyw = 3x– 5yzt + yzAlso find the velocity and acceleration of a fluid particle at (1, 0, 1) at time, t = 1 please answer fassssst
A flow is described by velocity V=ay i+bt j ,a=1s-¹ and b =.5m/s².at t=25s,what are the coordinates of the particle that passed through point (1,2) at t=24s?at t=26s, what are the coordinates of the particle that passed through point (1,2)?plot the pathline and streamline through point (1,2) and compare with streamlines through the same point at the instants t=24s,t=25s and t=26s.
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.
In a stream line steady flow, two points A and B on a stream line are 1 m apart and the flow velocity varies uniformly from 2 m/s to 5 m/s/ What is the acceleration of fluid B?