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-5 A steady, two-dimensional velocity field is given by
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Chapter 4 Solutions
Fluid Mechanics: Fundamentals and Applications
- Consider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis isarrow_forwardQ.5 The velocity components in x and y direction 2 are given by u = Axy° - xy; v = > ху; v — ху = xy² – 3/4 .4 y*. The value of A for a possible flow field involving an incompressible fluid is: A -3/4 В 3 C 4/3 D -4/3arrow_forwardProblem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.arrow_forward
- 4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk , V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?arrow_forward3.4 Consider a steady, incompressible, 2D velocity field for motion parallel to the X-axis with constant shear. The shear rate is du/dy Ay. Obtain an expression for the velocity field V. Calculate the rate of rotation. Evaluate the stream function %3D for this flow field. Ay Ay + В і, о, Ay + By+ C 6. Ans: V= 2arrow_forward5. The velocity field of an incompressible flow is given by V = (a1x + a2y + azz) i + (b1 x + b2y + b3 z)j + (c1x + c2y + c32)k, where a1=2 and c3=-4. The value of b2 isarrow_forward
- The 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_forward1. A flow in the x-y plane is given by the following velocity field: u =3 and v=6m/s for 0arrow_forwardIn three-dimensional fluid flow, the velocity component an u = * + y z, v = - (xy + yz + zx). Determine the %3D satisfy the continuity equation.arrow_forward2) A steady, incompressible, two-dimensional velocity field is given by V(u, v) = (2+2.5x + y)i + (1.5-3x - 2.5y)j where the x- and y-coordinates are in m and the magnitude of velocity is in m/s. a) Determine if there are any stagnation points in this flow field, and if so, where they are. b) Calculate the velocity at the point (x=2 m, y=3 m). c) Show whether the flow is rotational or irrotational? d) Calculate the vorticity. e) Calculate the shear strain rate in xy plane.arrow_forward2) A steady, incompressible, two-dimensional velocity field is given by V(u, v) = (2+2.5x + y)i + (1.5 — 3x − 2.5y)] where the x- and y-coordinates are in m and the magnitude of velocity is in m/s. a) Determine if there are any stagnation points in this flow field, and if so, where they are. b) Calculate the velocity at the point (x=2 m, y=3 m). c) Show whether the flow is rotational or irrotational? d) Calculate the vorticity. e) Calculate the shear strain rate in xy plane.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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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