The velocity field of incompressible flow in a Cartesian system is represented by V = 2 (2? – y?) î + vj + 3k Which one of the following expressions for v is valid?
Q: (b) Two velocity components of a steady, incompressible flow field are given as follows; и 3 2ах +…
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Q: d flow is represented by the velocity = 2xi + 4yj . The equation of stream line paSSI gh a point (2,…
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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: 3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric =…
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Q: 3.4 The stream function in a two dimensional flow field is given by y = x² - y? The magnitude of the…
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Q: 1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a…
A: Given: Solution : let (u ,v) are the component on velocity in x & y direction, respectively.…
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: Q3) The velocity field for a two dimensional steady and incompressible fluid flow given as: V =(-3x°…
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Q: 2. In a two dimensional incompressible fluid flow, the velocity components are given by: u=(x-4y)…
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Q: The velocity components in a two-dimensional flow are u = y^3 /3 + 2x-x²y and v= xy²-2y-x^3…
A: Data given- u = y3/3 + 2x-x2 y and v= xy2 -2y-x3 /3
Q: 3. The two-dimensional velocity field v = (3t- 8xy)i+ 4(y – x')j satisfies the Euler's equation of…
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Q: Show that the incompressible velocity potential in plane polar coordinates o(r, 0) is such that аф 1…
A: Velocity potential function is defined as a scalar function of space and time such that its negative…
Q: The velocity field of an incompressible flow is given by V = (a,x + a,y + azZ)i + (b,x + b,y + b3z)j…
A: Answer: The value of b2 is 2.
Q: In cylindrical polar coordinates (r, theta, z), the velocity components of a flow field are given as…
A: Given details: vr=r2zcosθ r=0.5mvθ=rzsinθ z=1mvz=z2t θ=π4 Formula…
Q: If stream function Y = 2xy, then the velocity at a point (1, 2) is equal to (а) 2 (c) /20 (b) 4 (d)…
A: Given, Stream function = ψ = 2xy x component of velocity is given by, u = ∂ψ∂y= ∂∂y (2xy)= 2x y…
Q: The equation of streamline passing through (1, 1) for the velocity function V = -y?i – 6xj is
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Q: For the velocity components given as : u = ay sin xy, v = ax sin xy. Obtain an expression for the…
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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: 4. Show that v = 3xi+ (t- 6xy)j is a possible fluid velocity fo unsteady flow of a homogeneous…
A: GivenV=3x2i+t-6xyjandF=6yti+18x2yj
Q: 5. The velocity field of an incompressible flow is given by V = (a1x + a2y + az z) i + (b1 x + b2y+…
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Q: The velocity field given by V = Axi-Ayj represents flow in a ngular corner. Evaluate the circulation…
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Q: Q3 (a) The compressible form of the continuity equation is (ap/at) + V.(pV) = 0 Expand this equation…
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Q: 2. The velocity field of a flow in cylindrical coordinates (r, 0, z) is u, = 0, ue = arz, u, = 0 %3D…
A: Solution: Given Data: The required parts (a), (b) and (c) are determined 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: The velocity components of an incompressible, two- dimensional velocity field are given by the…
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Q: Given the steady, incompressible velocity distribution V =3 x i + Cy j + 0 k , where C is a…
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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: Ca) A two-dimensional flow field is given by u = 5x² – 5y, = -10ry (i) Find the streamfunction & and…
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Q: Do the following velocity components represent physically possible flows ? u =x + z? + 5, v = y² +…
A: The feasibility of a fluid flow can be determined using the Continuity Equation, which is…
Q: Problem (5.9): In a three-dimensional incompressible fluid flow, the velocity components are u = x?…
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Q: The velocity vector in a flow is given by :V=-3xi-4yj-7zk Determine the stream equation passing…
A: The velocity vector in a flow is, V = -3x i - 4y j - 7z k The velocity components of equation are,…
Q: Q1 For a certain incompresible flow field, it is suggested that the velocity components are given by…
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Q: Two velocity components of a steady, incompressible flow field are given as follows; u = 2ax + bxy +…
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Q: HW2_Q3. Streamline. For the velocity field v*= 4i + where A = 2m?s', and the coordinates are…
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Q: The velocity flow field in a steady non-uniform flow is represented by the following equation,…
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Q: 2. A velocity field is given as U= = 3xy + t²,v=y+t² and w=1-zt² Determine local, convective and…
A: Acceleration is defined as the rate of change of velocity with respect to time.…
Q: The velocity field of a flow is described by…
A: Write the given velocity field for the flow. V→=4xi^+5y+3j^+3t2k^ Write the standard velocity field…
Q: If the stream function is y = 2xy, then the velocity at a point (1, 2) is equal to:
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Q: Q4: The velocity components for a two dimensional incompressible flow are - 6xy, v = -3x² + 3y2 1)…
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Q: Question 3 Consider the two-dimensional incompressible velocity potential O = xy + x? – y² a) Show…
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Q: For the velocity field in u = Ax , υ = By , and w = Cxy , the convectiveacceleration in the…
A: To find out the convective acceleration in the x-direction ax=ududx+vdudy+dudt
Q: The radial velocity component in an incompressible, two- dimensional flow field (v, = 0) is v, = 2r…
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Q: 29. Density of a two-dimensional steady compressible flow field in the Cartesian coordinate system…
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Q: Is the velocity field x,e, X,e2 X. 2. .2 isochoric?
A: In fluid mechanics, an isochoric flow is the one where the density of the fluid remains constant…
Q: Cinsider the 2-D steady flow field V=(2xy-5y2ji+(4x²+3xy)li The number of stagnation points in the…
A: Given:V=(2xy-5y2)i+(4x2+3xy)j
Q: H.W : a stream function is given by : Y = 2x?y + (x+t)y Find the velocity equation for fluid at time…
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Q: II ) The complex potential is w(z) = mln z - in which m is a given real constant, (1) What kinds of…
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Q: The velocity field of an incompressible flow in a Cartesian system is represer V = 2(x? – y² )i +…
A: Given:V→=2(x2-y2)i+vj+3k
Q: 1. What is the third velocity component such that continuity equation is satisfied if two components…
A: As per our guidelines, experts can provide solution to only one problem in case of multiple…
Q: Let the flow of a fluid of density ρ = 1000 kg m^-3 defined by the velocity field v = xy i + yz j +…
A: Irrotational Flow Note : What Is Asked Is Not Clear.
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- 1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.Numerical Problem: Round off your final answers into 2 decimals only. a) The velocity vector in a fluid flow is given as V = 1xt- 12x?yj + 3tk. Find the resultant velocity and acceleration of a fluid particle at (1,3,4) at time t=1. b) Determine the third component of velocity such that they satisfy the continuity equation: v = 3y and w = 1ryz?. c) Find the convective acceleration at the middle of a pipe which converges uniformly from 0.2 m diameter to 0.12 m diameter over 2 m length. The rate of flow is 30 liters per second.3.7 A steady, incompressible, inviscid 2D velocity field is given by .3 %3D 3 For what value of x and y, the field will represent irrotational flow if b- a= 64? [Ans: x = 8, y (any value)] %3D
- 3.11 For a 2D flow, the velocity potential function is given by =x - y, find the velocity at points (2, 2) and (2, 4). In addition, determine the flow rate between the streamlines passing through these points. [Ans: 4/2 units, 4/5 units, 8 units] 0 101.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP|B² Vz = 2µL B a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B? v, = 2μL Problems 11 - 2B --– €. (a) 2B (b) Figure 1.3. Flow between parallel plates. b) Calculate the volumetric flow rate by using the velocity distributions given above. What is your conclusion? 2|A P|B³W Answer: b) For both cases Q = 3µL1. Answer the following questions: (a) What is the physical meaning of the following: D a +V.v at Dt where V is the velocity vector of the flow field. (b) Let the viscous stress tensor be denoted by 7. How is the surface (vector) force f, acting by the fluid on a surface element ds (with unit normal în ) computed? Give your answer in vector notation and also in index notation. What is the physical meaning of Ty ? (c) Write down the work done on a material volume of fluid by the viscous surface force in vector notation and also in index notation. (d) Write down the amount of conduction heat flux 'q' (a scalar) on a surface element ds (with unit normal în ) in vector notation and also in index notation.
- A Fluid Mechanics, Third Edition - Free PDF Reader E3 Thumbnails 138 FLUID KINEMATICS Fluid Mechanies Fundamenteis and Applicationu acceleration); this term can be nonzero even for steady flows. It accounts for the effect of the fluid particle moving (advecting or convecting) to a new location in the flow, where the velocity field is different. For example, nunan A Çengel | John M. Cinbala consider steady flow of water through a garden hose nozzle (Fig. 4-8). We define steady in the Eulerian frame of reference to be when properties at any point in the flow field do not change with respect to time. Since the velocity at the exit of the nozzle is larger than that at the nozzle entrance, fluid particles clearly accelerate, even though the flow is steady. The accel- eration is nonzero because of the advective acceleration terms in Eq. 4-9. FLUID MECHANICS FIGURE 4-8 Flow of water through the nozzle of a garden hose illustrates that fluid par- Note that while the flow is steady from the…(b) One form of fluid movement is rotation and deform angularly. Figure Q1(b) shows the rotation and angular deformation caused by velocity variation about z-axis. Based on Table 1 and setting given to you, derive an equation of rotation. ди Sy St ây > B' ĉu B B ôy dy A' ↑ Sa v+. ôx A ôx Figure Q1(b) : Rotation and Angular Deformation Table 1: Axis of Rotation Setting Axis of Rotation 2 у-ахisA velocity field of the two-dimensional, time-dependent fluid flow is given by where t is time. Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any time t > 0 and any pont x > 0, y > 0. a) Incompressibility a) Is this flow incompressible (i.e. it has zero divergence)? Yes No ди Ət b) Time derivative of flow field Calculate the time derivative of the velocity. Represent your answer in the form i+ || 3 3 u(t, x, y) =r? (x² + y² ) i− {etxtyj X уј 3 a = c) Material derivative and acceleration Calculate the material derivative of the velocity and hence the acceleration a. Represent your answer in the form Du Dt || j i+ j
- 4-17 Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4-16. The pressure field is given by P = Po 2U,bx + b°(x² + y°) where P, is the pressure at x = 0. Generate an expression for the rate of change of pressure following a fluid particle.Consider the following three-dimensional velocity vector: V = 4xy² i + fj- z²y² k a) Find the appropriate form of the function f such that the velocity vector represents a physical incompressible flow. b) What is the stream function for this flow? c) Write down the expression for the velocity potential along the plane z = 0.Tp = Fq +°P/Q• (1) Here ip/Q is the "position of point P relative to point Q." Similarly the velocities of the two points are related by õp = bq + Up/Q- (2) The quantity õp/Q is the velocity of point P relative to point Q. I want you to use these ideas to solve the following problems. 1. The figure below shows a view from above of a large boat in the middle of the ocean. So that the crew on the ship can get exercise on long journeys, there is a circular walking/running track on the back deck. CA B- -D Suppose that the radius of the track is R = 6 m, and a person is running on the track at a constant speed of v = 3m/s as measured with a stopwatch by a crew-mate on board the ship. Suppose the runner is running counter-clockwise around the track when viewed from above. Write the velocity vector of the runner in terms of basis (ê1, ê2) as perceived by a crew-mate on the ship. (a) What is the velocity vector when the runner is at point A? (b) What is the velocity vector when the runner is…