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Consider the steady, two-dimensional, incompressible velocity field,
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Fluid Mechanics: Fundamentals and Applications
- 1. A Cartesian velocity field is defined by V = 2xi + 5yz2j − t3k. Find the divergence of the velocity field. Why is this an important quantity in fluid mechanics? 2. Is the flow field V = xi and ρ = x physically realizable? 3. For the flow field given in Cartesian coordinates by u = y2 , v = 2x, w = yt: (a) Is the flow one-, two-, or three-dimensional? (b) What is the x-component of the acceleration following a fluid particle? (c) What is the angle the streamline makes in the x-y plane at the point y = x = 1?arrow_forwardTwo velocity components of a steady, incompressible flow field are known: u = 2ax + bxy + cy2 and ? = axz − byz2, where a, b, and c are constants. Velocity component w is missing. Generate an expression for w as a function of x, y, and z.arrow_forwardA fluid has a velocity field defined by u = x + 2y and v = 4 -y. In the domain where x and y vary from -10 to 10, where is there a stagnation point? Units for u and v are in meters/second, and x and y are in meters. Ox = 2 m. y = 1 m x = 2 m, y = 0 No stagnation point exists x = -8 m, y = 4 m Ox = 1 m, y = -1 m QUESTION 6 A one-dimensional flow through a nozzle has a velocity field of u = 3x + 2. What is the acceleration of a fluid particle through the nozzle? Assume u, x and the acceleration are all in consistent units. O 3 du/dt 9x + 6 1.5 x2 + 2x O Oarrow_forward
- Fluid mechanics It is given as u=2 (1 + t), v=3 (1 + t), w=4 (1 + t) in a flow field. Accordingly, find the velocity and acceleration values at the points (3,2,4) at t = 2 seconds.arrow_forward1. For the following velocity fields, determine if they are possible for incompressible flows and if they are irrotational: (a) √ = î(x+y) + ĵ(x − y + z) + Ê(x + y +3) (b) ▼ = î(xy) + ĵ(yz) + k(yz + z²) (c) V = î[x(y +z)] + ĵ[y(x + z)] + k[−(x + y)z − z²] (d) V = î(xyzt) + ĵ(−xyzt²) + k[(z²/2) (xt² − yt)]arrow_forwardThe velocity components of a flow field are given by: = 2x² – xy + z², v = x² – 4xy + y², w = 2xy – yz + y² (i) Prove that it is a case of possible steady incompressible fluid flow (ii) Calculate the velocity and acceleration at the point (2,1,3)arrow_forward
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