The velocity field for a flow is given by: V (5x+ 6y+7z) i- (6x + 5y + 9z)j + (3x+ 2y + Az)k and the density veries as p = Po e. In order that the mass -21 is conserved, the value of A should be

Q: Consider the flow with velocity field given as (F·x)x 1 F- 8TTur u ( with Ha given constant, F a…

A: Given : To find : Do fluid particles rotate

Q: is shown the unsteady-state streamlines of a cylinder moving with a uniform velocity U in the fluid…

A: Part 2:Explanation:Step 1: Begin by understanding the problem statement, which describes a cylinder…

Q: 3.4 The stream function in a two dimensional flow field is given by y = x² - y? The magnitude of the…

A:

Q: The velocity components in the x and y directions 3 are given by u = Axy3 -x2y, v = xy² -y'. y*. The…

A: For solution refer below images. From the given datau=λxy3-x2y →velocity in x-directionv=xy2-34y4 →…

Q: An incompressible viscous flow is contained between two parallel plates separated from each other by…

A:

Q: If for a two-dimensional potential flow, the velocity potential is given by : 0 = 4.x(3y – 4),…

A:

Q: e vorticity

A: ZERO VORTICITY

Q: A two-dimensional incompressible velocity fi eld has u =K (1 - e - ay ), for x ≤ L and 0 ≤ y ≤ ∞.…

A: Write the expression for the continuity equation.

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: A two-dimensional flow field is given by u = 5x 2 − 5y 2v = −10xy (i) Find the streamfunction ψ and…

A:

Q: In a fluid rotated as a solid about a vertical axis with angular velocity ω, the pressure rise p in…

A: Given Data→Angular velocity=ωPressure rise=PPressure rise depends upon  speed ω, radius r, and fluid…

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: (d) Calculate the amount of a fluid per unit of time that crosses the paraboloid cylindrical S:…

A:

Q: Derive the Eulerian acceleration of a fluid particle in a flow field given by 1 V = xy²i -y'j + xyk

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: 3. Consider a fluid motion at a velocity = Voi with a space-time varying density such that, n(x, t)…

A:

Q: The velocity in a certain flow field is given by the equation below, V = (x² - y²)ī — 2xyj Show that…

A:

Q: The velocity field of an incompressible flow is given by V = (a1x + a2y + a3z)i + (b1a + b2y + bzz)j…

A: Given, V = ( a1x + a2y + a3z ) i + ( b1x + b2y + b3z  ) j + ( c1x + c2y + c3z ) k a1 = 2 c3 = -4…

Q: The stream function of a flow field is ų = Ax3 – Bxy², where A = 1 m-1s1 and B = 3 m1s1. (a) Derive…

A: The velocity along the x axis can be determined as shown below.

Q: velocity pe lace equati S..2 S.?

A: introduction: here we have to find out what type of flow

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

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: The velocity at apaint in aflwid for -- may be given in The Eukerian Coord A- Ax+ Bt , Show That x…

A: Write the given velocity profile in terms of the position.

Q: A flow can be described by the following equations. u =x cos y and v =-2x siny. Then flow is (A)…

A: Given:u=x2 cosyv=-2x siny

Q: Campute the Steady skte momentum Flex Eys b Alm? when the lower platevelecity v fn the Figure beloo…

A: Write the lower plate velocity.   v=0.304 m/s   Write the separation of the plate.   y=0.304…

Q: Determine the vorticity for the velocity field, u = 3x + 2y ,v = 5x – 3y %3D |

A: The components of the velocity field are given as, u=3x+2yv=5x-3y

Q: In deriving the continuity equation, we assumed, for simplicity,that the mass fl ow per unit area on…

A: Solution : Consider a cuboid of dimension dx ,dy &  dz as shown in figure below :

Q: A potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy .…

A: From given information:

Q: Question 2. In a particular fluid flow, the Eulerian velocity is given by u= (- x², 3xy, (3y -…

A: Given:The Eulerian velocity is .The density field is  and .Formula used:The flow is incompressible…

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: Ay j. Is this a possible case of incompres- 23 A velocity field is given by V = Axyi %3D sible flow?…

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: 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 velocity components in spherical coordinates of the axisymmetric uniform flow of a viscous fluid…

A:

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: 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: The velocity for a steady, incompressible flow in the xy plane is given by u=Ax?, v= Ayx, where A=…

A:

Q: Is of a uniform flow filed, a d-

A: False

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.