C (C is a constant)4xy)=xy-2y2+2x2+C (C is a constant)O C.O d. 4(xy)=xy3-2y2+2x2+C (C is a constant)ClearmychoiceThe stream function for a two-dimensional incompressible flow field is y = - 2(x-y), what isthe corresponding velocity potential equal?Oa.p = 2(x - y) + CO b. p = 2(x + y) + Cp = (x + y) + CO d. p = (x - y) + CClear my choiceConsider a steady two-dimensional, incompressible flow of a Newtonian fluid with the veloc-x and v = y – x, Find the pressure field P(x, y) if the pressure at point O (x= 0, y =field: u =is equal to PO and the velocity field satisfies the Navier-Stokes equations.

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

The stream function for a two-dimensional incompressible flow field is y = - 2(x-y), what is the corresponding velocity potential equal? P = 2(x - y) + C O b. p = 2(x + y) + C Oa. p = (x + y) + C O d. p = (x - y) + C Clear my choice

The stream function for a two-dimensional incompressible flow field is y = - 2(x-y), what is the corresponding velocity potential equal? P = 2(x - y) + C O b. p = 2(x + y) + C Oa. p = (x + y) + C O d. p = (x - y) + C Clear my choice

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

Similar questions

Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow
1. 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.
A Fluid Mechanics, Third Edition - Free PDF Reader E3 Thumbnails 138 FLUID KINEMATICS Fluid Mechanies Fundamenteis and Applicationu acceleration); this term can be nonzero even for steady flows. It accounts for the effect of the fluid particle moving (advecting or convecting) to a new location in the flow, where the velocity field is different. For example, nunan A Çengel | John M. Cinbala consider steady flow of water through a garden hose nozzle (Fig. 4-8). We define steady in the Eulerian frame of reference to be when properties at any point in the flow field do not change with respect to time. Since the velocity at the exit of the nozzle is larger than that at the nozzle entrance, fluid particles clearly accelerate, even though the flow is steady. The accel- eration is nonzero because of the advective acceleration terms in Eq. 4-9. FLUID MECHANICS FIGURE 4-8 Flow of water through the nozzle of a garden hose illustrates that fluid par- Note that while the flow is steady from the…
Use Eq. dx/u =dy/v=dz/w=dr/V to find and sketch the streamlines of the followingfl ow field:u = Kx; v = -Ky; w = 0, where K is a constant.
A velocity field of the two-dimensional, time-dependent fluid flow is given by where t is time. Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any time t > 0 and any pont x > 0, y > 0. a) Incompressibility a) Is this flow incompressible (i.e. it has zero divergence)? Yes No ди Ət b) Time derivative of flow field Calculate the time derivative of the velocity. Represent your answer in the form i+ || 3 3 u(t, x, y) =r? (x² + y² ) i− {etxtyj X уј 3 a = c) Material derivative and acceleration Calculate the material derivative of the velocity and hence the acceleration a. Represent your answer in the form Du Dt || j i+ j
CX a) Investigate whether the function o represents the velocity potential x²+y2 of a particular incompressible 2D flow, and if so, what should be the dimension of constant C which has value of 2.
The 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 difference
Consider the following three-dimensional velocity vector: V = 4xy² i + fj- z²y² k a) Find the appropriate form of the function f such that the velocity vector represents a physical incompressible flow. b) What is the stream function for this flow? c) Write down the expression for the velocity potential along the plane z = 0.
a) Consider steady and incompressible two-dimensional fluid flow field with a radial velocity component, Ur. The equation for the radial velocity component is: Ur = 5r² sine Determine the expression for the corresponding tangential velocity component, U required to satisfy the conservation of mass.
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?
An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.
a) Contsioer THE velbeine Fieb: V- xy i+ xyj (ij UNIT VECTORS AbNG X-, AND Y DIRECTTONS) IF THE FIUID DENSITY is CONOTANT, is CONSERVATION OF MASS SATİSFİED! CONSIDER THE FolbwiNG STREAM FUNCTION is THE Flow FielD IRROTATIONAL ? WHAT is THE VelocitY POTENTIAl ? C) CONSIDER THE STREAM FUNCTION DESCRIBING A Flow Field iN THE UPPER plaNE xy yoo. FOR THERE is A plATE @ y=0. ) i) is No-slip SATİS FIED @ PIATE (y=o) DRAW THE STREAMLINES FIND THE PRESSURE AS A FUNCTION OF THE PRESSURE O ORIGIN Po. (ASSOME NO GRAVitr).