Given the velocity field V = Axî – Ayĵ, where A = 4s-1, (a) Sketch the velocity field. (you can do this by hand or use software
Q: For each of the listed equations, write down the equation in vector form and decide if it is linear…
A: (a) For incompressible continuity equation : As there is no nonlinear term.
Q: (c) Consider the following steady, three-dimensional velocity field in Cartesian coordinates. V =…
A: The condition for the flow field to be incompressible: a = 24•c3
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Q: Converging duct flow is modeled by the steady, twodimensional velocity field V-›= (u, ? ) = (U0 +…
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Q: 5. A fluid flow in R3 has velocity field i = -x?i + xj + 2zk. (a) Find the equation of the field…
A: For solution refer below images.
Q: 6.33 In a certain two-dimensional flow field, the velocity is con- stant with components u = -4 ft/s…
A: We have to determine corresponding stream line
Q: A two-dimensional flow field in the xy plane is given by u = y v = x2+y2 x2+y2 are the velocity…
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Q: What is the velocity potential function? (i.e., ø =?) Please select one of the following…
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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: For a certain incompressible flow field it is suggested tl 2- velocity components are given by the…
A: For an incompressible flow... The divergence of the velocity vector mustbe zero..
Q: A steady, incompressible, two-dimensional velocity field is given by V-›= (u, ? ) =…
A: Given Data: The velocity field is given as V(u,v) = (2xy +1)i + (-y2 -0.6)j The angular velocity…
Q: A general equation for a steady, two-dimensional velocity field that is linear in both spatial…
A: The flow is steady, meaning that the fluid flow does not change with time. The velocity field is…
Q: Consider the following steady, two-dimensional, incompressible velocity field: V-› = (u, ? ) = (ax +…
A: The given velocity field is; V→=ui^+vj^=(ax+b)i^+(-ay+c)j^ The expression for the angular velocity…
Q: Given the following steady, two-dimensional velocity field. [Diberi medan halaju yang mantap dan dua…
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Q: A velocity field V = (x - 2y)ỉ - (2x + y)¡ given in the form. a)specify how many directions is the…
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Q: The velocity potential for a two-dimensional velocity field is given by the relation fi=(7/3)x3-7xy2…
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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: For a steady flow, the velocity field is V = (-2² + 3y) i + (2zy) j. The magnitude of the…
A: Given, V → = -x2 + 3y i^ + (2xy) j^ X and Y components of velocity is given by, u = -x2 + 3yv =…
Q: The velocity field given by V = Axi-Ayj represents flow in a ngular corner. Evaluate the circulation…
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Q: Velocity field V= (Ax)i - (Ay)j,x and y in meters. If A=0.3 s, find equation of the streamline in…
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Q: Consider the steady, two-dimensional, incompressible velocity field, V-› = (u, ?)=(ax + b) i-› +…
A: Given data: The steady incompressible two-dimensional velocity field is; V→=u,v=ax+bi→+-ay+cj→.…
Q: consider the 2 dimensional velocity field V= -Ayi +Axj where in this flow field does the speed…
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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: 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: Consider the following steady, two-dimensional, incompressible velocity field: V = (u, v) = (ax +…
A: solution: V=(u,v)=(ax+by2)i+(bx2-ay)ju =ax+by2v =…
Q: In a certain region of steady, two-dimensional, incompressible flow, the velocity field is given by…
A: Given: Two dimensional steady flow Incompressible flow V→= (u,v) =(ax +b)i→+ (-ay+ cx)j→ u= ax +b v=…
Q: Ca) A two-dimensional flow field is given by u = 5x² – 5y, = -10ry (i) Find the streamfunction & and…
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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 for a line vortex in the r?-plane is given byur = 0 u? = K / rwhere K is the…
A: The magnitude of the velocity is, So, the contour curves of constant speeds will be the circles of…
Q: Consider the steady, incompressible, two-dimensional velocity field V-›= (u, ? ) =…
A: The velocity field is given by Vx,y=4.35+0.655xi+-1.22-0.656yj The streamlines are given with…
Q: Question no-16 A velocity field is given by V. axí + byja baytk, where a= 25' , b 1m's'. Is it…
A: V=axi^+byj^+bxytk^a=2 , b= 1
Q: Consider the following steady, incompressible, two-dimensional velocity field: V = (u, v) = x²i +…
A: Given Data: It is a steady ,incompressible and two dimensional velocity field.
Q: A steady, two-dimensional velocity field is given byV-› = (u, ? )…
A: Given, The velocity field is, V→=u,v=2.85+1.26x-0.896yi→+3.45x+cx-1.26yj→ The flow is irrotational…
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: velocity field is given by 2xyi -yʻj. The streamlines for this flow are given by the family of…
A: Given , Two dimensional incompressible flow, Velocity field is given by=2xyi-y2 j so, we…
Q: A steady, two-dimensional velocity field in the xy-plane is given by V-›= (a + bx)i-›+…
A: Given, Velocity field V→=(a+bx) i^+(c+dy)j^+0 k^
Q: The velocity field of a flow is given by V axyi + by 2 j where a = 1 m-1s -1 and b = - 0.5 m-1s…
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Q: A fluid flow in R³ has velocity field i = -x²i+ xj+2zk. (a) Find the equation of the field line…
A: v→=-x2i+xj+2zk ^ dxdt=-x2dydt=xdzdt=2zdxdy=-x2x…
Q: A 2D velocity field is given by V = (u, v) = (2.5 - 1.9x, 0.65 + 0.9y), where the coordinates are in…
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Q: HW2_Q4. Streamline. For the velocity field: v*= Ax²î + Bxyĵ Where A = 1m¯ls¬1 В -1s-1 and the…
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Q: Question 2: Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob.…
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Q: A common flow encountered in practice is the crossflow of a fluid approaching a long cylinder of…
A: Consider the equation of velocity field equation : Consider the continuity equation for cylindrical…
Q: c. For a given velocity field calculate the constants a, b, and c such that the flow field is…
A: It is required to determine value of a,b,c for flow field to be irrotational
Q: Converging duct flow is modeled by the steady, two- dimensional velocity field is given by…
A:
Q: Question 4: A velocity field is given as below: =-3xî +3zk a) Determine if the flow filed is…
A: Given: The velocity field, v = (-3x)i+(3z)k
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- Dentrance x=0 uentrance FIGURE P4-21 u(x) lexit x = L Dexit 4-22 For the velocity field of Prob. 4-21, calculate the fluid acceleration along the diffuser centerline as a function of x and the given parameters. For L = 1.56 m, uentrance = 22.6 m/s, and exit = 17.5 m/s, calculate the acceleration at x = 0 and x = 1.0 m. Answers: 0, -96.4 m/s²Numerical 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.Consider how the new geometry in this problem affects the math/boundary condition/derivation. Both equations are listed!
- A 1:30 model of a ship is made. The real ship has a hull length of 130 m and travels at 7.9 m/s. Find the fraude number. If there is a dynamic similarity and froude # criterion applies, what should the velocity of the mdoel ship be?Please include a kinamatic diagram (one for velocity and one for acceleration). Please DO NOT solve this using velocity analysis (cartesian vector analysis i j k). I would like it to be solved using the IC scalar method as requested in the picture for the question. Thank you for your understanding. If you can solve it as soon as possible that would be great and I will give you a thumps up and positive feedback :)[Q6] (a) At this instant, find angular acceleration and angular velocity for CD using Absolute motion method. II- Relative motion method III- Show that results from both methods are identical 10 m/s a-16 m/s 300 mm 3 mm (b) Find work done in a process in which P(V-0.6)*-10 When volume is changed from 0.2 m to 1.5 m
- Orange JO A O X 91|4 2:26 ch1_introductio.. Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A Water responds to shear stress by continuously yielding in angular deformation in the direction of the shear. IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear Istress, as shown in Figure 1.1. do dt dx ,and v = dy dx Angular deformation (Shear strain), 0 = dt do Rate of shear strain = dt dx dv (Velocity gradient) dy dy dt dv Therefore, to dv T = constant dy dv T = - dy The proportionally constant, u, is called the absolute viscosity of the flyid Example A flat plate of 50 cm² is being pulled over a fixed flat surface at a constant velocity of 45 cm/sec (Figure 1.1). An oil film of unknown viscosity separates the plate and the fixed surface by a distance of 0.1 cm. The force (T) required to pull the plate is measured to be 31.7 N, and the viscosity E of the fluid is constant. Determine the viscosity (absolute). 22 Example A flat…1. 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.The moment of the torpedo control unit in water was tested with a 1:8 scale scale model in a water tunnel of identical properties with a speed of 20 m/s if the measured moment in the model was 14 Nm. calculate 1) Determine the velocity of the prototype using the Reynolds number analogy. 2) Find the ratio of the forces occurring in the model and prototype. Using the analogy of Euler number 3) find the moment that occurred with the prototype.
- Cauchy's ΣF ) equation of motion : pDV/Dt =pg + VT (like pa Newtonian viscous stress relations by the tensor relation : Ti j = - pôij + µ[Əvj/əxi + əvi/axj] where dij is the kroneker delta function (1 for i = T includes pressure and viscous surface forces. into Cauchy's equation, and assume constant viscosity, to get the Navier-Stokes vector eq'ns : pDV/Dt Pg -vp + μ^2 V the acceleration DV/Dt av/at+ (VV)V, which for steady state flow gives DV/Dt =(V.) V. Because (VV) V is a non-linear term on the LHS of the N-S equation Reynolds Number RepVL/μ, a measure of the ratio of inertial to viscous forces. : Patm 10^5 = = N = N = ; pwater 1000; pair 1.2; μwater 10^-3 N s/m^2 ; Hair 2 x 10^-5 N•s/m^2 ; g 9.8 m/s^2 = j; 0 for i j ); N(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-ахisTp = 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…