Concept explainers
A velocity field is given by
(a ) Is this flow steady or unsteady? Is it two- or three-dimensional?
(b ) At (x,y,z) = (3.2,-3), compute the velocity
(c) At (x.y.z) = (3,2,-3), compute the heal (i.e., unsteady part) of the acceleration vector.
(d) At (x,y,z) = (3,2,-3), compute the convective (or advective) part of the acceleration vector.(e) At (x,y,z) = (3,2,-3), compute the (total) acceleration vector.
(a)
That the flow is steady or unsteady and is it two or three dimensional.
Answer to Problem 121P
The flow is steady and two-dimensional.
Explanation of Solution
Given information:
The velocity field is
Write the expression for the streamline for three- dimensional flow.
Here, the derivative of
Substitute
Conclusion:
The flow is steady and two-dimensional.
(b)
The velocity vector at
Answer to Problem 121P
The velocity vector is
Explanation of Solution
Write the expression for the velocity vector.
Here,
Substitute
Here, the location points are x, and y.
Calculation:
Substitute
Conclusion:
The velocity vector is
(c)
The local (unsteady part) of the acceleration vector at
Answer to Problem 121P
The local (unsteady part) of the acceleration is
Explanation of Solution
Write the expression for the local acceleration of the flow in
Here, the time derivative of
Write the expression for the local acceleration of the flow in
Here, the time derivative of
Write the expression for the local acceleration of the flow in
Here, the time derivative of
Substitute
Substitute
Substitute
Conclusion:
The local (unsteady part) of the acceleration is
(d)
The convective (or advective) part of the acceleration vector at
Answer to Problem 121P
The convective part of acceleration in
Explanation of Solution
Given information:
The velocity field is
Write the expression for the convective part of acceleration in
Here, the velocity component in
Substitute
Here, the location points are
Write the expression for the convective part of acceleration in
Here, the velocity component in
Substitute
Write the expression for the convective part of acceleration in
Here, the velocity component in
Substitute
Calculation:
Substitute
Substitute
(e)
The (total) acceleration vector at
Answer to Problem 121P
The total acceleration is
Explanation of Solution
Write the expression for the total acceleration.
Here, acceleration in
Calculation:
Substitute
Conclusion:
The total acceleration is
Want to see more full solutions like this?
Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
- 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.arrow_forward4s-1, Given the velocity field V = Axî – Ayĵ, where A %3D (a) Sketch the velocity field. (you can do this by hand or use software of your choice)arrow_forwardQuestion 3 (a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y > 0 is defined as: v = -Upxy i+ Upxy j where i and j are the unit vectors in the x- and y-directions respectively and Uo is a constant with units m/s. (i) Determine the magnitude and direction of the velocity at the point (1,1). (ii) Find the equation of the streamlines.arrow_forward
- Velocity Field Assignment 4 2 -5 -4 2 -1 N -4 W- E Consider the steady, two-dimensional velocity field of wind as: V= (u, v)= (8 – 0.5x)i + (0.5 - 5y)j where x- an y- coordinates are in m, time in s, and the magnitude of the velocity is in m/s. Determine: (a) A stagnation point, if existed. (b) Sketch the velocity vector for the given coordinate on the map. (c) Sketch the relevant streamlines on a different graph. (d) Verify if the flow is rotational or irrotational flow. (e) Looking at the velocity vector, which section of the country will receive the most rain if the wind brings rainy season from the south-china sea?arrow_forward4. A steady, incompressible, and two-dimensional velocity field is given by the following components in the xy-plane: Vxu = 2.65 + 3.12x + 5.46y = Vy= =v=0.8+ 5.89x² + 1.48y = Calculate the acceleration field (find expressions for acceleration components ax and ay and calculate the acceleration at the point (x,y) = (-1,3).arrow_forward1. 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.arrow_forward
- (2) Consider the following fluid velocity fields: F(x,y) = (x,y), F(x,y)=(-x, y), F(x,y) = (y, 0). (a) Plot the three fields as glyphs. Which of these vector fields represent an expansion, a compression and a shear flow? (b) Calculate the divergence of the three fields V F. Can you relate the value of the divergence with the nature (compression, expansion or shear of the flow)? (c) Calculate the circulation V x F and relate it with the nature of the flow.arrow_forwardA incompressible, steady, velocity field is given by the following components in the x-y plane: u = 0.205 + 0.97x + 0.851y ; v = v0 + 0.5953x - 0.97y How would I calculated the acceleration field (ax and ay), and the acceleration at the point, v0= -1.050 ? Any help would be greatly appreciated :)arrow_forwardThe velocity potential for non-viscous two-dimensional and uncompressed water flow in Cartesian coordinates is given as D= -(3x²y - y³) a) Find the corresponding current function. b) Find the pressure difference between points (1,2) and (4,4). Omit the height differencearrow_forward
- A steady, incompressible, two-dimensional velocity field is given by V = (u, v) = (0.5 +0.8x) 7+ (1.5-0.8y)] Calculate the material acceleration at the point (X=3 cm, y = 5 cm).arrow_forward(a) Given the following steady, two-dimensional velocity field. [Diberi medan halaju yang mantap dan dua dimensi.] V = (u, v) = (8x + 6)ï + (-8y – 4)j (i) Is this flow field an incompressible flow? Prove your answer. (ii) Is this flow field irrotational? Prove your answer. (iii) Generate an expression for the velocity potential function if applicable.arrow_forward1. 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 + 2y2jarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY