1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible flows, where is Stokes' stream function, and u = VxS, uz = S(r, z, t) = where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence 1 d4 r dr 1 dy r dz Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads Y(R, 0, t) R sin UR S(R, 0,t) = = Y(r, z, t) r Ug = and Ur = 1 ay R² sin de 1 ӘҺ R sin 0 OR ∙eq, 9

1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible flows, where is Stokes' stream function, and u = VxS, uz = S(r, z, t) = where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence 1 d4 r dr 1 dy r dz Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads Y(R, 0, t) R sin UR S(R, 0,t) = = Y(r, z, t) r Ug = and Ur = 1 ay R² sin de 1 ӘҺ R sin 0 OR ∙eq, 9

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: A velocity field is given by u = 5y2, v = 3x, w = 0. (a) Is this flow steady or unsteady? Is it…

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

Q: An Eulerian velocity vector field is described by V = 3xzj + yk, where i, j and k are unit vectors…

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

Q: 2] Consider the following stedy, incompressible, two-dimensional velocity field: V=(u,v)=(0.5+1.2x)…

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: Does the two-dimensional incompressible flow given by u(x, y) = c₁ - c)+4cy xy 1(x, y) = 1 2c₁₁√(x²…

A: Compute Partial Derivative of u(x,y) with respect to x:Compute Partial Derivative of v(x,y) with…

Q: A fluid has a velocity field defined by u = x + 2y and v = 4 - y. In the domain where x and y vary…

A: Since you have posted a multiple independent question, we will solve first question for you. To get…

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: Question 2. In fluid dynamics, a "stagnation point" in a moving fluid is a point where the veld the…

A: To find: A non constant velocity vector field in R2 having stagnation point at 1,2.

Q: For a certain two-dimensional incompressible flow, velocity field is given by 2xy î - yj. The…

Q: Given the following steady, two-dimensional velocity field. [Diberi medan halaju yang mantap dan dua…

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

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

Q: Fluid flows in a converging nozzle Area of the nozzle: A=Ao*(1-b*x) Entry speed:…

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

Q: An Eulerian velocity vector field is described by V = 2i + yz2tj −z3t3k, where i, j and k are…

A: given: “Since you have asked multiple question, we will solve the first question for you. If you…

Q: Use the mass continuity equation to derive an expression for the vertical velocity at the top of a…

A: for the above question the answer is Zero(0)

Q: The stream function for a two-dimensional incompressible flow field is y = - 2(x-y), what is the…

A: given; →stream function (ψ)=-(x-y)→velocity potential function(ϕ)=?

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

1. For incompressible flows, their velocity field
2. In the case of axisymmetric 2D incompressible flows,
where is Stokes' stream function, and
u = VXS,
S(r, z, t) =
Uz =
where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence
1 Ꭷ
r dr
1 dy
r dz
Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads
Y(R, 0, t)
R sin 0
S(R, 0, t)
UR
uo
Y(r, z, t)
r
=
=
-eq,
and
Up = =
1
ay
R2 sin Ꮎ ᎧᎾ
1 ƏY
R sin Ꮎ ᎧR
-eq
2
(1)
(2)
(3)

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: Given data

VIEW

Step 2: Derivation of Velocity Components in Spherical Coordinates

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 8 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

Converging duct flow is modeled by the steady, two- dimensional velocity field V = (u, v) = (U₁ + bx) i-by. For the case in which Ug = 3.56 ft/s and b = 7.66 s¯¹, plot several streamlines from x = 0 ft to 5 ft and y=-2 ft to 2 ft. Be sure to show the direction of the streamlines. (Please upload you response/solution using the controls provided below.)
A 2-D, incompressible, flow field has an x-component of flow, u = 2xy² if the velocity at (1,2) is(8,12); What is the velocity at (2,3)?
The flow field about a rotating cylinder with the radius a can be modelled by superimposing the velocity potentials of a uniform flow filed, a doublet and a potential vortex: p = Ux[1+ (a/r)²] – (TO)/(2x) Does this velocity potential satisfy the Laplace equation? True False
I am working on a practice exam and I wanted to be certain if I was going about the problem correctly.
Fluid mechanics
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
Question 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.
PLS SHOW ME FULL STEPS SIR PLS ANSWER WITHIN 30 MIN SIR SUBJECT (FLUID MECH 2)
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
A fluid flows along a flat surface parallel to the x-direction. The velocity u varies linearly with y, the distance from the wall, so that u = ky. (a) Find the stream function for this flow. (b) Is this flow irrotational?
navier stokes
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 ?