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A steady, two-dimensional velocity field is given by
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Fox and McDonald's Introduction to Fluid Mechanics
- 4. A steady, incompressible, and two-dimensional velocity field is given by the following components in the xy-plane: Vxu = 2.65 + 3.12x + 5.46y = Vy= =v=0.8+ 5.89x² + 1.48y = Calculate the acceleration field (find expressions for acceleration components ax and ay and calculate the acceleration at the point (x,y) = (-1,3).arrow_forward1. 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.arrow_forwardAnswer question 3 in the attached image pleasearrow_forward
- By equation (3) we find ( a= 368 Problem: A flow field is defined by u = 3y , v= 2 x y .w = 4 z. Derive expressions for the x, y , and z components of acceleration. Find the magnitude of the velocity and acceleration at the point ( 1,2,1) Specify units in terms of (L and T).arrow_forwardvelocity field is given by: A two-dimensional V = (x - 2y) i- (2x + y)Ĵj a. Show that the flow is incompressible and irrotational. b. Derive the expression for the velocity potential, (x,y). c. Derive the expression for the stream function, 4(x,y).arrow_forward6)arrow_forward
- Need correctly.arrow_forward1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.arrow_forwarda. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.arrow_forward
- Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 sarrow_forwardAssumptions The flow is steady. The flow is incompressible. The flow is two-dimensional in the x-y plane V = (u, v) = (U, + bx) ỉ - byj %3D We are to calculate the material acceleration for a given velocity field. (None = b( U, +bx) a. y b? y = b( U, +by) ax b2 x (Uo +bx) = b y a, IIarrow_forwardQ1) One dimensional steady fluid flow along x axis is shown in figure. The velocities at point O and X2 as from uo= 3 m/s and u2= 12 m/s. Assuming that the velocity is varying linearly with the distance through x axis, Uo= 3 m/s U2= 12 m/s X, +0.10 m- a) Calculate accelerations at O, X, and X2 points. (15) b) Determine the flow is incompressible or not. (10) 0.20 m-arrow_forward
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