Sources of equal strength m are placed at the four symmetricpositions (x, y) = (a, a), (-a, a), (-a, -a), and (a, -a).Sketch the streamline and potential line patterns. Do anyplane “walls” appear?

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

A:

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: When the components of velocity are : -ay ax w =C u= Show that the streamlines ( 4 = constant) are…

A: Derived the stream lines are helices on the circular cylinders.

Q: A flow field u = 2x, v = 3y. Find the magnitude of acceleration at the point (1, 2).

A: Given:u=2xv=3yP(1,2)

Q: Determine the complex potential of two line vortices of the same strength k , one located at the…

A: complex potential for a single line vortex located at the origin: W= ikln(z)Strength= kLocated at…

Q: e vorticity

A: ZERO VORTICITY

Q: Investigate the complex potential f(z) = A cosh [π(z/a)],and plot the streamlines inside the region…

A: Writing the complex potential function: Where A is a constant.   Splitting the potential function…

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

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Q: Q3/ Prove that in a two dimensional fluid flow, the stream function: -xy is harmonic. = zk+zx

A: Given dataStream function  φ=-xyx2+y2To prove the given stream function is harmonic in two…

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

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

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Q: Calculate the effort (F) that has to be applied in the pulley system

A: As shown in figure , m=100 kg is loaded at pulleysthen tension on role is…

Q: For the stream function Y = r5/2 sin streamlines of this flow. 50 2 calculate the pressure field and…

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

A: Givenu=x2v=-2yx

Q: Q.3Given the x and y velocity components below (A is a constant): u = Axt v = -Ayt (a) Find the…

A: We have to determine (a) Find the equation of the streamlines, also give the stream function. (b)…

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

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

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Q: Consider a flow field represented by the stream function y = (4+6) x'y - (6+6) x²y² + (4+6) xy. Is…

A: Given data: The stream function is ψ=10x3y-12x2y2+10xy3

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

A: Checking if flow is irrotational.

Q: at A on the wall.

A: Answer= 14m/s

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: Problem 3: Obtaining the stream function from velocity components The steady state, incompressible…

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Q: Find the stream function associated with the two-dimensional incompressible, possible flow with…

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Q: Proof that Streamlines and equipotential lines are orthogonal to each other

A: Stream function ψψ=fx,y so now partially differentiating dψ=∂ψ∂xdx+∂ψ∂ydy Now by defination of…

Q: Q1:- (a) Show that stream function exists as a consequence of equation of continuity. (b) Show that…

A: (a) Consider the stream function ψx,y,t. For two dimensional flow the velocity in the terms of…

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

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

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Q: Question 4. The stream function is given as w=x³-y³. a. Is this flow possible? b. Is the flow…

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

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Q: Consider three equally spaced sources of strength mplaced at (x, y) = (+a, 0), (0, 0), and (-a, 0).…

A: The pattern resulting stream lines as shown below. There are two stagnation points at x = ±a3 =…

Q: If u = ax and v = ay and w = -2az obtain equation of streamline passing through the point (2, 2,4)…

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Q: A uniform stream of speed V is inclined at angle ? from the x-axis . The flow is steady, two-dimen…

A: A stream function is defined as the scalar function of space and time such that its partial…

Q: (a) [(-2, 1,0), (5, 3, -1), (8, –5, 2)), (b) [(8,-5, 2), (5, 3, –1), (–2, 1,0)), (c) [(1,-1,0), (2,…

A: given data: V = 3i +0j -k according to the rules, we can only answer up to 3 parts so solving 3…

Q: whether the function o represents the velocity potential %3D x2+y2 lar incompressible 2D flow, and…

A: ∅=cxx2+y2 c=2Now for φ to represent velocity potential of incompressible 2D flow…

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.