3. The two-dimensional velocity field v = (3t- 8xy)i+ 4(y – x')j satisfies the Euler's equation of motion of a homogeneous incompressible fluid. Assuming no body forces, determine the pressure, p(x, y,t) at any point.

3. The two-dimensional velocity field v = (3t- 8xy)i+ 4(y – x')j satisfies the Euler's equation of motion of a homogeneous incompressible fluid. Assuming no body forces, determine the pressure, p(x, y,t) at any point.

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: The flow of a particular fluid is described by a velocity field given as u = x²y v = x³ = xy² w = 0…

Q: Consider a three-dimensional, steady velocity field given by V = (u, v, w) = (3.2 + 1.4x)ï + (2.4 –…

A: Write the expression of velocity field. V=3.2+1.4xi+2.4-2.1yj+wk Write the components of…

Q: 1 du du, Nij 2 дх, дх 2. The rate-of rotation tensor is defined as - and the vorticity of the…

A: For solution refer below images.

Q: The velocity components in the x and y directions 3 are given by u = Axy3 -x2y, v = xy² -y'. y*. The…

A: For solution refer below images. From the given datau=λxy3-x2y →velocity in x-directionv=xy2-34y4 →…

Q: Q3) The velocity field for a two dimensional steady and incompressible fluid flow given as: V =(-3x°…

Q: 2. In a two dimensional incompressible fluid flow, the velocity components are given by: u=(x-4y)…

Q: If for a two-dimensional potential flow, the velocity potential is given by : 0 = 4.x(3y – 4),…

Q: A 2D incompressible velocity field is defined by . If both u and v are 0 at point (x = 0, y = 0),…

A: Given Data: The flow is 2D and incompressible. The flow is defined as u=2(x2-y2). The pressure and…

Q: 2. Consider the Eulerian velocity field u(x, t) = y i+ (x – sin t) j, where x = x i+yj and t is the…

A: A) Vx= cos(t) Vy= x dy/dx= (x/ cos(t)). Integrating this we get. y*cos(t)= x2/2 +C. By…

Q: A velocity field is described by the following equations: 10y -10x U = x²+y2 V = x2+y2' and w=0 (a)…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: There is an incompressible Newtoniel fluid between the parallel plates whose bottom plate is fixed…

A: Consider a plate as shown in the figure which is flowing over the fluid. The bottom fluid is fixed.…

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: A velocity profile for water is given as a function of x, y and z. How can we determine if the…

Q: The bottom plate is fixed, the top plate is moved by V speed between parallel plates There is an…

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: Consider the velocity field V 10x x2+y2 10y 2ty), where coordinates are measured in meters. a)…

A: Given velocity field:V→=10xx2+y2i¯+10yx2+y2j¯This implies :u=10xx2+y2v=10yx2+y2a) For…

Q: The flow of a particular fluid is described by a velocity field given a u = x²y v = x³ = xy² w = 0…

Q: At t = 0, an unstable velocity field V = xy²ti + zxj – t³k, emerges in the 3D plane as a result of a…

A: Given : V=xy2ti+zxj-t3k To find : Equation of streamline

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: Q No. 1: The streamlines associated with a certain fluid flow are represented by a family of curves…

A: given:Stream lines associated with a certain fluid flow are represented by a family of…

Q: The flow of a particular fluid is described by a velocity field given as u = x²y v = x³ = xy² w = 0…

Q: 3- The velocity components in a three dimensional fluid flow are: U=x'+y°z? , v=-(xy+yz+zx)…

A: We are suppose to solve only one question. Please post other question as a separate question.

Q: The stream function is given by y =-4xy. Then the magnitude of velocity at point (2,4) m/s.

A: Given Stream function = -4xy Point = 2,4 Find Magnitude of velocity, V

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: 4. The viscosity of incompressible viscous fluid is u = 0.96m Pa s. The velocity field is given by:…

A: Fluid is a substance that deform continuously under the action of shear stress no matter how small…

Q: 5. The velocity field of an incompressible flow is given by V = (a1x + a2y + az z) i + (b1 x + b2y+…

Q: Consider a steady, two dimensional, incompressible flow of a Newtonian fluid velocity field: u =…

A: Given Data,u=-2xyv=y2-x2Mass conservation must be statisfied_∂U∂x+∂v∂y=0∂-2xy∂x+∂∂yy2-x2=-2y+2y=0

Q: The no-slip condition, pressure force is a component of the molecular stress tensor. O A. vanishing…

Q: 2. The velocity field of a flow in cylindrical coordinates (r, 0, z) is u, = 0, ue = arz, u, = 0 %3D…

A: Solution: Given Data: The required parts (a), (b) and (c) are determined below:

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

Q: The velocity field of 2-D steady incompressible flow is given by V= yi-xj Determine the circulation…

A: Note:As per our guidelines we are supposed to answer only one question. Kindly repost other…

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

A: Writing the continuity equation for the two-dimensional velocity field for an incompressible flow…

Q: 2. The y component of velocity in a steady, incompressible flow field in the xy plane is 3xy(x²- y?)…

A: Let x component be u For incompressible flow ∂u∂x+∂v∂y=0∴∂u∂x=-∂v∂y

Q: Question5b: The velocity components for an incompressible steady flow field are u= (5 x' +2z°) and…

Q: B. a. An incompressible, inviscid fluid flows steadily past a ball of radius R, as shown in the…

Q: in the x-y plane; In a steady, 2D, incompressible flow, there is a velocity field defined as…

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

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

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: A two-dimensional flow field has velocities along the x and y directions given by u = x't and v = -…

A: Given, x component of fluid velocity = u = x2 t y component of fluid velocity = v = -2xyt Equation…

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: The radial velocity component in an incompressible, two- dimensional flow field (v, = 0) is v, = 2r…

Q: Consider the velocity field represented by V = K(vĩ + xk) Rotation about z-axis is

Q: Is the velocity field x,e, X,e2 X. 2. .2 isochoric?

A: In fluid mechanics, an isochoric flow is the one where the density of the fluid remains constant…

Q: In three-dimensional fluid flow, the velocity component an u=x + y z, V =- (xy +yz + ZX). Determine…

A: Given data: u=x2+y2z2v=-xy+yz+zx Need to determine the value of "w".

Q: The velocity components in the x and directions are given by y 3 u = Axy3 - x2y, v = xy? The value…

A: Given, x component of velocity = u = λ xy3 - x2y y component of velocity = v = x y2 - 34 y4 For…

Q: The velocity field of an incompressible flow in a Cartesian system is represer V = 2(x? – y² )i +…

A: Given:V→=2(x2-y2)i+vj+3k

Concept explainers

Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing. 

Question

Answer question 3 in the attached image please

2. Calculate the circulation of the flow v=-8xyi+ 4 y j around the triangle with
vertices (0, 0), (3, 0), (3, 2).
3. The two-dimensional velocity field
v = (3t-8xy)i+ 4(y – x )j
satisfies the Euler's equation of motion of a homogeneous incompressible fluid.
Assuming no body forces, determine the pressure, p(x, y, t) at any point.

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 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

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.
Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). Calculate the vorticity.
The expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.
for the following flows, find the equation of the streamline through(1,1). v= -y^(2)i-6xj
Consider the steady, incompressible, two-dimensional velocity field V= (u, ) = (0.5 + 0.8x) i+ (1.5 - 0.8y) j. Calculate the material acceleration at the point (x = 2 m, y = 3 m). (b) Sketch the material acceleration vectors.
Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). For the velocity field given , calculate the circulation around a circular path of radius 5 m. Assume that u and v given are in units of meters per second.
Find the stream lines and path lines of the particles of the two dimensional velocity field u=\frac{x|1+t}, v=y, w=0.
The velocity vector in a flow is given by :V=-3xi-4yj-7zk Determine the stream equation passing through a point L(4,2,3)
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 2D incompressible velocity field is defined by . If both u and v are 0 at point (x = 0, y = 0), determine a) v component of the velocity and b) an expression for pressure field. Assume gravity is in the – y-direction and pressure is 0 at point (x=0, y=0). The flow is defined by: u=2(x2-y2)
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.