Consider a steady, two dimensional, incompressible flow of a Newtonian fluid velocity field: u = -2xy v = y² – x² a) Show that this flow model satisfies the continuity relation. b) Obtain expressions for the fluid accelerations in the x and y directions. c) Find the pressure distribution P(x, y) , if the pressure at the point x = y = 0 is Po. Neglect gravity.

Consider a steady, two dimensional, incompressible flow of a Newtonian fluid velocity field: u = -2xy v = y² – x² a) Show that this flow model satisfies the continuity relation. b) Obtain expressions for the fluid accelerations in the x and y directions. c) Find the pressure distribution P(x, y) , if the pressure at the point x = y = 0 is Po. Neglect gravity.

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: 6.26 The velocity components in an ideal, two-dimensional velocity field are given by the equations…

Q: For a given hypothetical flow the velocity at time t = 0 to t = 10 s was u = 0, v = 4m/s. Then from…

Q: 3.1. The velocity at a point in a fluid for a one-dimensional flow may be given in the Eulerian…

A: The last line means that: x is a function of x0 and t in Lagrange coordinates. Please Rate if…

Q: A simple approximate velocity field for this flow of the Converging duct flow is modeled by the…

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

Q: Please check this step-by-step and correct if wrong:

Q: 4. A steady, incompressible, and two-dimensional velocity field is given by the following components…

A: The step by step solution is provided below.

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: For the following velocity field, determine the constant a for having an incompressible fluid flow.…

Q: a).Show that the UNSTEADY velocity field given below represents a 2-dimensional incompressible flow.…

A: Given V→=(xyt3-yt2)i+(x-y2t3/2)j u=(xyt3-yt2)v=(x-y2t3/2) to prove that velocity is in 2D

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

Q: A simple flow model for a two-dimensional converging nozzle is the distribution u= U. (1+) v = − U₁7…

Q: 4. Briefly describe die casting process and name 2 types.

A: Die casting process: It is a type of metal casting process in which the molten metal is forced into…

Q: 3. The velocity components of a two-dimensional incompressible fluid flow are prescribed as v=-3x²…

Q: Verify whether or not the following difference representation for the continuity equation for a 2-D…

Q: Q5: A/ Consider the flow field given in Eulerian description by the expression q =( x+2y+a )i…

A: GIVEN DATA - A VELOCITY FIELD GIVEN WE HAVE TO FIND Z-COMPONENT OF VELOCITY

Q: Problem 3: Obtaining the stream function from velocity components The steady state, incompressible…

Q: 1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible…

Q: 1) A steady, incompressible, two-dimensional velocity field is given by the following components in…

Q: 2. Consider the two-dimensional time-dependent velocity field u(x, t) = (sint, cost, 0), in the…

A: Given:The velocity field,

Q: Find the vorticity of the fluid motion for the given velocity com- ponents. KINEMATICS OF FLUIDS (a)…

Q: A CFD model of steady two-dimensional incompressible flow has printed out the values of velocity…

Q: Consider a 2-dimensional incompressible flow field. The vertical component of velocity for the flow…

A: We can answer up to 3 subparts so we will answer first 3. Please resubmit the question by specifying…

Q: Consider the incompressible, irrotational, 2D flow. where the stream function is given by: 4 = 424…

A: Given: φ=4zy Solution: (a) The velocity field is given as : v=∂φ∂z=∂∂z(4zy)=4yw=-∂φ∂y=-∂∂y(4zy)=-4z…

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

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

Please answer both
6.7 A one-dimensional flow is described by the velocity field u = ay + by² v = w = 0 where a and b are constants. Is the flow irrotational? For what com- bination of constants (if any) will the rate of angular deformation be zero?
3.3 Verify whether or not the following difference representation for the continuity equation for a 2-D steady incompressible flow has the conservation property: (u, 1.j + u;41.j-1 - u.; – 4j.j-1) (1,j – 41,j-1) 2 Ax Ay where u and v are the x and y components of velocity, respectively. 3.4 Repeat Prob. 3.3, for the following difference representation for the continuity equation: (4i+ 1,5 - Uj-1,) (u, j+1 - V,j-1) + 2 Ax 2 Ay
a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.
4. Consider the steady, two-dimensional velocity field given by: u = 2xy-y²; v=x-y². Show that it is a possible 2d incompressible flow. Find the component of acceleration in x direction of a fluid particle at point (x, y) = (1,2)
A flow field is given by V=x^2*yi+ y^2*zj−(2xyz+ y z^2) k(a) Prove that it is a case of possible steady incompressible fluid flow (clue: use continuity equation)(b) Calculate the velocity and acceleration at the point (2,1,3)
36 Chapter 2 Force Systems 2/23 Determine the resultant R of the two forces shown by (a) applying the parallelogram rule for vector addition and (b) summing scalar components. 60° 400 N Problem 2/23 2/24 It is desired to remove the spike from the timber by horizontal axis. An obstruc-
Question 3 Consider the two-dimensional incompressible velocity potential O = xy + x² – y2 a) Show that this flow is irrotational. b) Find the stream function Y(x, y), if Y(0,0) = 0 .
In plane stagnation flow, an incompressible fluid occupying the space y>0 has one velocity component given by Vx-x. The flow is two-dimensional and steady, such that V₂=0 and nothing depends on z or time t. (a) Use the continuity equation to determine Vy(x,y), given that Vy(x,0) =0. (This condition for Vy corresponds to the plane y=0 being an impenetrable boundary.) (b) is arbitrary, so you may set Y=0 at any convenient location.) Determine the stream function for this flow, (x,y). (The absolute value of
Please complete this question ASAP. This question doesn't have a diagram and I keep getting stuck. I need this done within an hour and a half. Thanks.
THREE DIMENSIONAL ( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).
How would I calculate the fluid acceleration along the nozzle centerline. Here, there is steady flow of water through an axisymmetric garden hose nozzle and alongthe centerline the water speed increases from uentrance to uexit . The centerline water speed increases parabolically through the nozzle. What would be an equation for centerline speed u(x), based on the parameters given in the drawing from x = 0 to x = L ?