2.9 A velocity field is specified as V=axyi+by²j, where a = 2m ¹s ¹, b=-6 m-¹s-¹, and the coordinates are measured in meters. Is the flow field one-, two-, or three-dimensional? Why? Calculate the velocity components at the point (2, 1/2). Develop an equation for the streamline passing through this point. Plot several streamlines in the first quadrant including the one that passes through the point (2,¹/2).

Q: Check if o = x - y + y represents the velocity potential for 2-dimensional irrotational flow. If it…

A:

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

A:

Q: In a certain two‐dimensional flow field, the velocity is constant with components u = –4 ft/s and v…

A: to find:the velocity potential function  for the flow fieldthe stream function for the flow…

Q: 3. The two-dimensional velocity field v = (3t- 8xy)i+ 4(y – x')j satisfies the Euler's equation of…

A:

Q: The x and y components of velocity for 2D flow are u=6y ft/s, and ??=3 ft/s, where y in feel.…

A: Given data: u=6y ft/s v =3 ft/s Need to determine the  equation of streamline.

Q: Consider a steady, two-dimensional, incompressible velocity field with u = aX +b and V--ay + Cx,…

A: Given data:

Q: An equation for the velocity for a 2D planar converging nozzle is w = 0 Where U is the speed of the…

A: Given: Velocity in x direction is, u=U1+xL Velocity in y-direction is, v=-UyL

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

A:

Q: Sketch the stream lines represented by y = xy. Also find out the velocity and its direction at point…

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: Determine that the given flow field is rotational or irrotational. If r- determine the axes of…

A: Givenu=x2v=-2yx

Q: Consider a steady two-dimensional flow with the velocity field in the Cartesian coordinate system is…

A: Given, u=-Ax v=Ay A is constant

Q: Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and…

A: Given that :Flow is two dimensional flowVelocity field terms are given u=1v=2ytAsking to calculate…

Q: In a 2D dimension incompressible flow , if the fluid velocity components are given by u = x-4y , v =…

A: Given:The fluid velocity components are given as:u=x-4yv=-4x

Q: A 2-D flow field has velocity components along X-axis and y-axis given by u = x't and v = -2 xyt…

A:

Q: 2-D unsteady flow field has the velocity components: v = - x²y?t u = - Plot the streamline passing…

A:

Q: The velocity potential for a two-dimensional velocity field is given by the relation fi=(7/3)x3-7xy2…

A:

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

A:

Q: A 2D velocity field is given by V = (u, v) = (2.7 - 1.9x, 0.7 + 1.6y), where the coordinates are in…

A:

Q: A velocity fi eld is given by u = V cos θ , v = V sin θ , andw = 0, where V and θ are constants.…

A: Given Data: The velocity in x direction u = V cosθ. The velocity in y direction v = V sinθ. 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) Determine the fluid acceleration at x-4, y-5. (b) Determine the rate of volumetric dilatation in…

A:

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

A:

Q: A flow is described by velocity V=ay i+bt j ,a=1s-¹ and b =.5m/s².at t=25s,what are the coordinates…

A: we know thatVelocity V=dydtdydt=btdy=bt.dtintegrating both sides we get∫y0ydy=∫t0tbt.dty-yo=br220t

Q: Given the vector equation below for velocity of a given fluid: V=(0.5+1.2x)i + (-2.0-1.2y)j, derive…

A:

Q: A 2D velocity field is given by V = (u, v) = (0.9 + 1.85x, 1.4 - 1.6y), where the coordinates are in…

A: The calculated sum of x and y components of the velocity at the point (1, 2 ).

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: onal flow field is give

A: given: φ=x2-y2

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: Ux = -ax Uy = ay  Using the streamline equations show the streamlines of the flow as well as stating…

A: Given data ux=-axuy=ay Here, ux and uy is the speed of the flow in X and Y direction. Now we have to…

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

A: The velocity vector can be compared with  V→= ui^ +vj^  u = axy = xy v= by^2 = -0.5y^2 since both…

Q: A unifom flow field defined by y - y is superposed on u=xi-yj. Determine the stream function and…

A: The above question relates to kinematic of fluid flow.

Q: A velocity field is given by u-V cosa, v= V sinx and w=0. The equation for streamline will be: y=x…

A: Option A is correct

Q: a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. . i. Find…

A: The component of velocity in the x-direction is u=2x+y. The component of velocity in the y-direction…

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.