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A steady, three-dimensional velocity field is given by
Calculate constants a, b, and c such that the flow field is irrotational.
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Fluid Mechanics: Fundamentals and Applications
- 4. Consider a velocity field V = K(yi + ak) where K is a constant. The vorticity, z , is (A) -K (B) K (C) -K/2 (D) K/2arrow_forward1.6 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 = 3µLarrow_forward1) A steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane: V(u, v) = (0.25 +1.4x + 0.8y)i + (-0.5 +0.9x - 1.4y)] where the x- and y-coordinates are in m and the magnitude of velocity is in m/s. a) Calculate the acceleration field (find expressions for acceleration components ax and ay) b) Calculate the acceleration at the point (x, y) = (2, 3).arrow_forward
- The velocity field for a fluid flow is given by following expression: =(0.2x² + 2y+2.5)î +(0.5x+2y² – 6) ĵ+(0.15x² + 3y° + z)k The strain tensor at (2,1,–1) will be: 0.8 1.25 0.30 a) | -1.25 -4 0.30 -1 (0.8 1.25 0.70 b) | 1.25 2 0.30 -2 1 0.8 1.25 0.30) c) | 1.25 4 -2 0.30 -2 1 0.8 1.25 0.30 d) | 1.25 8. -2 0.8 2 1arrow_forwardConsider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis isarrow_forwardy x = r cos 0 V = Or y = r sine r = √x² + y² χ Flow in "solid body rotation" acts like a solid spinning around an axis. The streamlines are circular, the velocity is purely tangential, and the velocity magnitude is V = r, where is the angular velocity (positive counter-clockwise) and r is the radius. (a) Express the velocity vector V as a function of x and y. (b) Calculate the curl of the velocity vector V × V, indicating clearly the direction of the resulting vector.arrow_forward
- Q.2 A flow is described by the stream function v = 25xv, The coordinates of the point at which velocity vector has a magnitude of 4 units and makes an angle 150 ° with the X-axis is A x=1.0, y=0.5774 B X=0.5774, Y=1.0 WRONG C X=1, Y=-0.5774 D X=-1, Y=0.5774arrow_forwardA flow is uniform if the parameters describing the flow vary with distance along the flow path. TRUE FALSEarrow_forwardHelp me pleasearrow_forward
- two-dimensional velocity field u =xt + 2y and v =xt^2- yt x=1 meter y= 1 meter and t= 1 second Find the acceleration where it is.?arrow_forward1. For a two-dimensional, incompressible flow, the x-component of velocity is given by u = xy2 . Find the simplest y-component of the velocity that will satisfy the continuity equation. 2. Find the y-component of velocity of an incompressible two-dimensional flow if the x-component is given by u = 15 − 2xy. Along the x-axis, v = 0.arrow_forwardIf the velocity field, V=3y2 i. Which of the following is NOT TRUE? Select one: The flow is steady The flow is irrotational The flow is horizontal d. The flow is incompressible Consider the velocity field, V=(x2+y2-4)i+(xy-y)j. Which of the following is not a stagnation point? A stagnation point is a point in the velocity field where the velocity is 0. (2, 0) (-2, 0) (1, √3) (-1, √3)arrow_forward
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