Consider the two-dimensional velocity field given by V = (5+ a₁x+b₁y) + (4+ a2x + b²y)Ĵ, where a₁, b1, a2 and 62 are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?

Q: for the following flows, find the equation of the streamline through(1,1). v= -y^(2)i-6xj

A: Given:Velocity vector, V=-y2 i-6 x jPositio of point, x, y=1, 1Find:The equation of streamline

Q: Consider a three-dimensional, steady velocity field given by V = (u, v, w) = (3.2 + 1.4x)ï + (2.4 –…

A: Write the expression of velocity field.   V=3.2+1.4xi+2.4-2.1yj+wk   Write the components of…

Q: Consider the two-dimensional velocity field given by V = (5+ a1x +b1y)i + (4 + azx + b2y)j, where…

A: Given, Two dimensional velocity field = V → = (5 + a1x + b1y) i^ + (4 + a2 x + b2 y) j^   From…

Q: The velocity components are given by in the following case u =x' +y +z, v =-xy- yz -x Find the third…

A: Given: u=x3+y+zv=-x2y-yz-x

Q: y = 2r'sin20 (2) 0.5 m A 2D inviscid incompressible fluid flow around a corner is In addition, if…

A: Given:- stream function ψ=2r2sin2θ, where ψ has units of ms2,r is in meters. fluid density=103kgm2…

Q: 1 du du, Nij 2 дх, дх 2. The rate-of rotation tensor is defined as - and the vorticity of the…

A: For solution refer below images.

Q: 3.3. The velocities at a point in a fluid in the Eulerian system are given by ux+y+z+s =2(x + y + z)…

A: Please Rate if this solution helps youThank You

Q: A 2D incompressible velocity field is defined by . If both u and v are 0 at point (x = 0, y = 0),…

A: Given Data: The flow is 2D and incompressible. The flow is defined as u=2(x2-y2). The pressure and…

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: lot the velocity field, potential field, and streamlines. Please explain it in detail.

A:

Q: coordinates are in meters. Determine whether the flow field is three-, two-, or one-dimensional.…

A:

Q: A steady, three-dimensional velocity field is given by V = (0.657 +1.73x +0.948y+as) + (2.61 +cr…

A:

Q: A two-dimensional flow field has velocities along x2t and the x and y directions given by u = V =…

A: Given data: u=x2tv=-2xyt Need to determine the streamline equation.

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

A:

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

A:

Q: 1. A flow in the x-y plane is given by the following velocity field: u-3 and v=6m/s for 0<t<20s;…

A: a)In the given problem, for the given particle released at t= 0 s,and u = 3m/s and v = 6 m/sDuring…

Q: The stream function is given by y =-4xy. Then the magnitude of velocity at point (2,4) m/s.

A: Given   Stream function = -4xy                    Point = 2,4 Find  Magnitude of velocity, V

Q: Consider the two-dimensional velocity field given by V = (5+ a₁x + b₁y)î + (4+ a2x + b²y)Ĵ, where…

A: Two dimensional velocity field = From velocity field, X-component of velocity = u=5+a1x+b1y…

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

A:

Q: For a steady flow, the velocity field is V = (-2² + 3y) i + (2zy) j. The magnitude of the…

A: Given, V → = -x2 + 3y i^ + (2xy) j^   X and Y components of velocity is given by, u = -x2 + 3yv =…

Q: The value of b,

A: Given; The velocity field of an incompressible flow is given in question: Where, a1=2…

Q: v=2r + 3r²sine

A: Consider a particle having position r which is changing with respect to time t. Let vr and vθ be the…

Q: A two - dimensional velocity field is given as V = -2yi – 2xj Find the current function 4(x,y) of…

A: Given  V = - 2y i - 2x j   To determine  the current function ψ(x,y) of the velocity field  and the…

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

A: Write the given data with suitable variables. V→=axy i^+by2 j^a=1 m-1s-1b=-0.5 m-1s-1

Q: A flow is described by velocity field, V=ayi+btj, where a=1 s-1and b=0.5 m/s2.At t=n s (Where n is…

A: Given: The expression of velocity is V=ayi+btj. Here, a=1 s-1and b=0.5 m/s2. n = 19

Q: A velocity field is given as V (x,y,z,t)=(5xy^2+t) I+ (2z+8) j+18 k. Here x,y and z are in metres…

A:

Q: eam function is given by u = 3 xy. Determine (i) The velocity function u, eration component at (1,…

A:

Q: The inlet pressure to a piping system is 440 kPa. The inlet pipe diameter is 0.6 m. What is the…

A:

Q: 4. Show that the velocity field V = 2y(2x + 1)î + [x(x+1) – 2y²1j represents a possible…

A:

Q: The stream function for a given 2D flow fields is V = 5x²y – (s/3)y Determine the corresponding…

A: Given data Stream function,ψ = 5x2y  - s3y3 We have to find the corresponding velocity potential.

Q: The stream function in a two dimensional flow field is given by  sie= x2 - y2  .find the magnitude…

A: Given data: ψ=x2-y2 Need to determine the magnitude of the velocity at point (1,1) .

Q: 6. For a two-dimensional flow, the velocity field is ū = 12 jwhere i and j are the basis vectors in…

A:

Q: An unsteady, incompressible, velocity field is given by the following vector: V = (u, v, w) = (−7t…

A: Velocity vector, V→=u,v,w=-7t+3.5xy+2.2yi→+2t+3x-1.6yj→+5+4zk→Point, x,y,z,t=-1,2,1,2

Q: The stream function for a given two-dimensional flow field is = 5x²y - 5y³. Determine the velocity…

A: First check whether flow is irrotational or not.because velocity potential function is only defined…

Q: Find the stagnation point in the following two-dimensional velocity field: V=(3+x-y)i + (5+x+y)j

A:

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.