A steady, incompressible, two-dimensional velocity field is given by            V-›= (u, ? ) = (2.5 − 1.6 x) i-›+ (0.7 + 1.6y) j-› where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. The shear strain rate in s−1 is (a) −1.6 (b) 1.6 (c) 2.5 (d ) 0.7 (e) 0

Q: How many Potechially defferent mixed tensors forder two can be defined Ex:0 by faking the ouler…

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Q: Question 3 Water flows in the vicinity of a 90° corner as shown in Figure 2. The flow could be…

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Q: Use the following figures to derive the Newtonian fluid shear stress formula. Why fluids governed by…

A: As per Newton's Law of viscosity : The shear stress is proportional to shear strain. τ=μdγdt here,γ…

Q: V = Vx ((r+ yz)i)

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Q: The Reynolds transport theorem (RTT) is discussed in Chap. 4 of your textbook. For the general case…

A: Step 1: Step 2: Step 3: Step 4:

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: A two-dimensional Cauchy stress tensor is given as o=t@n₁+ anı n2, where t is an arbitrary vector…

A: σ = t ⊗ n1 + α n1 ⊗ n2

Q: If the velocity field is (₂) ³ (x3 what is the stationary point (x,y)? FOR CREDIT, INCLUDE…

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Q: The thrust P of a propeller depends upon diameter (D); speed (u) through a fluid density (p);…

A: Given data: P = f (D,u,N,ρ,μ)   To determine: The above mentioned non-dimensional correlation

Q: The Navier-Stokes equations are the set of differential (vector) equations describing the motion of…

A: For solution refer below images.

Q: For the following velocity field, determine the constant a for having an incompressible fluid flow.…

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Q: The fluid flow in the region above the two planes: y = x and y = -x can be approximated by the…

A: Remark: As per the guidelines of BNED, only the first three subparts will be answered. You can ask…

Q: At any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70 volcanoes…

A: This problem is related to fluid mechanics. Fluid mechanics is the subject of mechanical engineering…

Q: Q2. For the following velocity distribution between 2 plates, calculate the force required to move…

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Q: Consider the velocity field, V = (x – 2y)i – (2x + y) j. What is the value of the velocity potential…

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Q: Angular momentum, also called moment of momentum (H->), is formed by the cross product of a…

A: The angular momentum is given by, The dimensional formula of angular momentum in SI unit,

Q: Calculate the material acceleration for the following steady, incompressible velocity field:

A: Given: Velocity fieldV→=0.5+0.8xi^+1.5-0.8yj^

Q: Q1. The material time derivative in the x and y direction for a 2D flow are given by: Dv Du du du du…

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

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Q: Consider the velocity field f= 2xi - y} A) Get an equation for flow lines. B)Draw a flow line…

A: Velocity components of fluid in x and y directions: u=2x v=-y

Q: . Determine the displacement gradient tensor, right Cauchy-Green deformation tensor, small…

A: Given: u=AX12X3BX1X2X3CX2+CX32 To find: Displacement gradient tensor Right Cauchy-Green deformation…

Q: A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V…

A: V=-2xyi+y2-x2ju=-2xy v=y2-x2

Q: 1. If u 3x*yt and v- -6x'y*t° answer the following questions giving reasons, Is this flow or fluid:…

A: a. if the flow satisfy the continuity equation then it said to be possible flow ∂u∂x+∂v∂y=0…

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

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Q: 1. Which of the following functions could represent the velocity potential for the two- dimensional…

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Q: The velocity potential for non-viscous two-dimensional and uncompressed water flow in Cartesian…

A: Given,  Velocity potential function φ = -3x2y + y3   Part (a): To find the current function, first…

Q: Bernoulli's Equation If the body forces are conservative and flow is of the potential kind, then the…

A: Euler's equation∂q∂t+12∇q2-q∧curlq = F-1ρ∇p  Curl of the function defines the rotation of the fluid…

Q: Derive an equation for volumetric strain rate and use it to verify that the following velocity field…

A: Given velocity field  V = (uo+bx)i-byj Find the volumetric strain rate and verify that its…

Q: 2. Consider the two-dimensional time-dependent velocity field u(x, t) = (sint, cost, 0), in the…

A: Given:The velocity field,

Q: Assumptions: The flow is steady, The flow is incompressible, The flow is two-dimensional in the x-y…

A: Solution:

Q: CX a) Investigate whether the function represents the velocity potential x²+y2 of a particular…

A: Write the expression of the function. ϕ=cxx2+y2   Partially differentiate the above function with…

Q: In an experiment to determine the force acting on an oval-shaped body, a model is mounted in the…

A: Solution: Given Data:   To Find: The total force acting on the model.

Q: It is given that the two dimensional velocity field of a fluid flow can be expressed as: V = (u, v)…

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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: A velocity field v=ui + vj + wk is given as: u =x+2y+3z + 4r°,v= xyz +t and w= (x+ y)z* +21.…

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Q: 2. The y component of velocity in a steady, incompressible flow field in the xy plane is 3xy(x²- y?)…

A: Let x component be u     For incompressible flow             ∂u∂x+∂v∂y=0∴∂u∂x=-∂v∂y

Q: (c) In the two-dimensional boundary layer, shear stress was changed linearly from the solid surface…

A: The equation of displacement thickness:  δ* = ( δ / 9 )

Q: The Ekman number, important in physical oceanography,is a dimensionless combination of μ , L , ρ ,…

A: The Ekman number can be represented as follows: E=fμ,L,ρ,Ω

Q: The Cauchy stress tensor for a (compressible) Newtonian fluid is given by S(x, t) = -p(x, t)I + X (V…

A: Write the Cauchy stress tensor for a compressible Newtonian fluid. Sx,t=-px,t∥+λ∇·vx,t∥+2μsym∇vx,t

Q: [7] Given the following stress tensor in Cartesian coordinates: [2.74 -2.12 3.69 Sym (a) Find the…

A: σ=2.74-2.124.07-2.123.69-3.024.07-3.025.05*103kPa

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.