(Problem 2.4) Consider the following velocity field: Uo(x²-y²+x)ex - U₁(2xy + y)ey (a) Compute the acceleration at y = 1 and x = 0 and x = 2. U₁ = 2 m s¹. (b) Compute the volumetric flow rate through the plane at x = 5 and extending from y = 0 to y= 5 and width 3 in the z direction.

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.?

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Converging 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.)

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).

Question 3 (a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y > 0 is defined as: v = -Upxy i+ Upxy j where i and j are the unit vectors in the x- and y-directions respectively and Uo is a constant with units m/s. (i) Determine the magnitude and direction of the velocity at the point (1,1). (ii) Find the equation of the streamlines.

xG 2. Find the rate of deformation for a line vortex with velocity field V=YG -Î+ x² + y² x² + y² Ans. Ex = -6 yy = 2xyG (x² + y² ) ² ¹ ² = ,&_= 0,& xyG (x² + y²)² ¹6 = -,&=&₁ = 0 -), G=const.

Q: A flow field is given by: V = (x'y)i+(y°z)j–-(2x*yz+ yz*)k Prove that it is a case of possible steady incompressible fluid flow. Calculate the velocity and acceleration at the point (3,2.4).

(2) Consider the following fluid velocity fields: F(x,y) = (x,y), F(x,y)=(-x, y), F(x,y) = (y, 0). (a) Plot the three fields as glyphs. Which of these vector fields represent an expansion, a compression and a shear flow? (b) Calculate the divergence of the three fields V F. Can you relate the value of the divergence with the nature (compression, expansion or shear of the flow)? (c) Calculate the circulation V x F and relate it with the nature of the flow.