Answered: velocity field v = t2 (x2y, xy2) in…

velocity field v = t2 (x2y, xy2) in cartesian plane. 1. is the flow compresible or incompresible? 2. Find a streamfunction of the flow. 3. Find the pattern of

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: An Eulerian velocity vector field is described by V = 2x2yi − 2xy2j − 4xyk, where i, j…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: A fluid flow is represented by the velocity = 2x+4y. The equation of stream line passing through a…

A: To find: The equation of stream line passing through the point 2,4. Given: The fluid flow…

Q: Stream function of the 2D flow is given as Y =x² + y² a. Find the velocity components for each…

A: Stream function is defined as the partial derivative with respect to any direction that gives the…

Q: unsteady velocity field V = xy'ti + zxj – t°k exists at the 3D plane along a streamline that passes…

Q: Consider the following steady, incompressible, two- dimensional velocity field: V = (u, v) = (4.35 +…

Q: 3 Starting with a small fluid element of volume dx dy dz, derive the continuity equation (Eq. 3.4)…

A: Given data To derive the continuity equation

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

A: Given, Stream function = Ψ = x2 - y2 Velocity in x-direction can be given by, u = - ∂ψ∂y= -∂∂y x2…

Q: Stream function: Y+coshx (a) Show if the function is incompressible. (b) Draw in Excel streamline…

A: The route of imaginary particles floating in the fluid and transported along with it is known as a…

Q: For incompressible flow, density remains the same Select one: True False

A: Incompressible fluid: A fluid whose density remains constant during any process or flow.

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: A velocity field is described (in Cartesian coordinates) by u = 2−x3/3, v = x2y−zt, w =…

A: solution given u=2-x3/3 , v=x2y-zt , w=0(a) ay=∂v∂xu+∂v∂yv+∂v∂zw+∂v∂t

Q: An incompressible plane flow has the velocity components u = - 4y2 , v = - 8x 1) Check whether the…

A: Incompressible flow In fluid mechanics or more generally continuum mechanics, incompressible flow…

Q: rectangular coordinates VX=XY2, VY=-X2Y, VZ=0 and ρ=xy. Make sure the velocity and density…

Q: The velocity field of a two-dimensional incompressible flow is given by u= kv (x? + y?) v = -kx/(x?…

Q: 03: A/ a stream function is given by: 4 = 2x'y+(x+t)y² .Find the velocity equation for fluid at the…

Q: The velocity components of a flow field are given by: u = 2x² – xy + z², v = x² – 4xy + y², w = 2xy…

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: A steady, incompressible, two-dimensional velocity field is given by the following components in the…

A: Given Data: The x-component of velocity is u = 0.205+0.97x+0.851y. The y-component of velocity is v…

Q: Velocity field V= (Ax)i - (Ay)j,x and y in meters. If A=0.3 s, find equation of the streamline in…

Q: Use Eq. dx/u =dy/v=dz/w=dr/V to find and sketch the streamlines of the followingfl ow field:u = Kx;…

A: Given Data: The x-component of velocity is u = Kx. The y-component of the velocity is v = -Ky. The…

Q: A two-dimensional, incompressible flow has the velocitycomponents u = 4 y and v = 2 x . ( a ) Find…

A: The velocity vector is independent of time and z-direction components. so X-direction acceleration…

Q: A steady incompressible, two-dimensional velocity field is given by: V(и, v) — (2х — у -5)1 + (3х —…

A: Given that, V →u,v=2x-y-5i^+3x-2y-8j^u=2x-y-5v=3x-2y-8 (i) The velocity at stagnation point is…

Q: CX a) Investigate whether the function represents the velocity potential x²+y2 of a particular…

A: Write the expression of the function. ϕ=cxx2+y2 Partially differentiate the above function with…

Q: It is given that the two dimensional velocity field of a fluid flow can be expressed as: V = (u, v)…

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: 3.4 Consider a steady, incompressible, 2D velocity field for motion parallel to the x-axis with…

A: Given: The shear rate , dudy=Ay

Q: velocity field V=xy^2 ti+zxj-t^3 k exists at the 3D plane along a streamline that passes through the…

Q: A steady, incompressible, two-dimensional velocity field is given by the following components in the…

A: Given, Steady, Incompressible and 2D flow. u = 1.85 + 2.05x + 0.656y m/s v = 0.754 - 2.18x - 2.05y…

Q: The stream function relation is given as: Y = xy Find the equations for the components of velocity.…

Q: The flow field of a fluid is given by V xyi + 2yzj - (yz + i) Show that it represent a possible…

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

A: The velocity vector can be compared with V→= ui^ +vj^ u = axy = xy v= by^2 = -0.5y^2 since both…

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

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

Q: I am working on a practice exam and I wanted to be certain if I was going about the problem…

A: V= x3sin y i + 3x2cos y j To find: Whether stream function is exist or not stream function pressure…

Q: Consider the steady, incompressible, two-dimensional velocity field V-›= (u, ? ) = (1 +…

A: Given data: Steady incompressible, two-dimensional velocity field…

Q: a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. . i. Find…

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

Q: whether the function o represents the velocity potential %3D x2+y2 lar incompressible 2D flow, and…

A: ∅=cxx2+y2 c=2Now for φ to represent velocity potential of incompressible 2D flow…

Q: Question1: An unsteady, incompressible, two-dimensional velocity field is given by the following…

Q: For V(x, y) = ri –- yj do three things: (i) sketch the vector field, (ii) solve the differential…

Q: -5 -4 +2 -1 W- E Consider the steady, two-dimensional velocity field of wind as: V= (u,v)= (8 –…

Q: Under what condition are all the three curves; pathline, streakline and streamline, the same

A: question Under what condition are all the three curves; pathline, streakline streamline, the same

Q: A fluid flow is described (in Cartesian coordinates) by u = x2, v = 4xz. (a) Is this flow…

A: Given:u=x2v=4xzThese are velocity vectors

Q: Consider the steady, two-dimensional velocity field of wind as: V= (u,v)= (8 – 0.5x)i + (0.5 - 5y)j…

Q: Question 2: Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob.…

Q: An unsteady velocity field V = xy²ti + zxj – t°k exists at the 3D plane along a streamline that…

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

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

An unsteady flow has velocity field v = t² (x²y, xy²) in cartesian plane.

1. is the flow compresible or incompresible?

2. Find a streamfunction of the flow.

3. Find the pattern of instantaneous streamline for the flow.

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 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

A two-dimensional, incompressible flow has the velocitycomponents u = 4 y and v = 2 x . ( a ) Find the accelerationcomponents. ( b ) Is the vector acceleration radial? ( c ) Sketcha few streamlines in the first quadrant and determine if anyare straight lines.
for the following flows, find the equation of the streamline through(1,1). v= -y^(2)i-6xj
The flow of an incompressible §uid is defined by u=3, v=9x. Does a stream function exist for this flow? If so, determine the expression for the stream function,Ψ.
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.
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
For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0: (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the x-component of the acceleration vector.
1. Find the stream function for a parallel flow of uniform velocity V0 making an angle α with the x-axis. 2. A certain flow field is described by the stream function ψ = xy. (a) Sketch the flow field. (b) Find the x and y velocity components at [0, 0], [1, 1], [∞, 0], and [4, 1]. (c) Find the volume flow rate per unit width flowing between the streamlines passing through points [0, 0] and [1, 1], and points [1, 2] and [5, 3].
(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. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.
In a 2D dimension incompressible flow , if the fluid velocity components are given by u = x-4y , v = -4x then stream function y is given by
A two-dimensional flow field has an x-component of velocity given in Cartesian coordinates by u = 2x − 3y. (a) Find v, the y-component of velocity, if the flow is incompressible and v = 0 when x = 0. (b) If the flow follows the Bernoulli equation, find an expression for the pressure distribution as a function of x and y, given that the pressure is p0 at the stagnation point.
A fluid flow is described (in Cartesian coordinates) by u = x2, v = 4xz. (a) Is this flow two-dimensional or three-dimensional? (b) Is this flow field steady or unsteady? (c) Find the simplest form of the z-component of velocity if the flow is incompressible.