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Fluid Mechanics: Fundamentals and Applications
- Velocity Field Assignment 4 2 -5 -4 2 -1 N -4 W- E Consider the steady, two-dimensional velocity field of wind as: V= (u, v)= (8 – 0.5x)i + (0.5 - 5y)j where x- an y- coordinates are in m, time in s, and the magnitude of the velocity is in m/s. Determine: (a) A stagnation point, if existed. (b) Sketch the velocity vector for the given coordinate on the map. (c) Sketch the relevant streamlines on a different graph. (d) Verify if the flow is rotational or irrotational flow. (e) Looking at the velocity vector, which section of the country will receive the most rain if the wind brings rainy season from the south-china sea?arrow_forwardAn incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.arrow_forward4. 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_forward
- 1. If u- 3x'yr and v = -6x'y'r answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1). %3Darrow_forwardConverging duct flow is modeled by the steady, two- dimensional velocity field V = (u, v) = (U₁ + bx) i-by. For the case in which Ug = 3.56 ft/s and b = 7.66 s¯¹, plot several streamlines from x = 0 ft to 5 ft and y=-2 ft to 2 ft. Be sure to show the direction of the streamlines. (Please upload you response/solution using the controls provided below.)arrow_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
- 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_forwardThe velocity potential function (0) is given by an expression xy' x'y x* + 3 3 (i) Find the velocity components in x and y direction. (ii) Show that o represents a possible case of flow.arrow_forwardDerive an equation for volumetric strain rate and use it to verify that the following velocity field is incompressible: V=(uo+bx)i-byjarrow_forward
- The velocity field for a line vortex in the r?-plane is given byur = 0 u? = K / rwhere K is the line vortex strength. For the case with K = 1.5 m/s2, plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.arrow_forwardA fluid flow is described (in Cartesian coordinates) by u = x2, v = 4xz. (a) Is this flow two-dimensional or three-dimensional? (b) Is this flow field steady or unsteady? (c) Find the simplest form of the z-component of velocity if the flow is incompressible.arrow_forwardAy j. Is this a possible case of incompres- 3.9 A velocity field is given by V= Axyi -- %3D sible flow? If yes, obtain the stream function and find the value of constant A for which the flow rate between the streamlines passing through the points (3, 3) and (3, 4) is 18 units. Axy Ans: V = 12 + C, A 7 2arrow_forward
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