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The velocity field for a line some in the
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Fluid Mechanics: Fundamentals and Applications
- 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_forwardConsider the steady, two-dimensional, incompressible velocity field, namely, V-›= (u, ?) = (ax + b) i-›+ (−ay + cx) j-›. Calculate the pressure as a function of x and y.arrow_forwardThe stream function in a two-dimensional flow field is given by y=x²- y². Then the magnitude of velocity at point (1, 1) isarrow_forward
- A steady, two-dimensional velocity field is given byV-› = (u, ? ) = (2.85 + 1.26x − 0.896y) i-› + (3.45x + cx − 1.26y) j-› Calculate constant c such that the flow field is irrotational.arrow_forward(a) A two-dimensional flow field is given byu = 5x 2 − 5y 2v = −10xy(i) Find the streamfunction ψ and velocity potential φ.(ii) Find the equation for the streamline and potential line which passesthrough the point (1, 1).arrow_forwardConverging duct flow is modeled by the steady, two- dimensional velocity field is given by V-›= (u, ? ) = (U0 + bx) i-›− byj-›. The pressure field is given byP = P0 −ρ/2 [2U0 bx + b2(x2 + y2)] where P0 is the pressure at x = 0. Generate an expression for the rate of change of pressure following a fluid particle.arrow_forward
- An Eulerian velocity vector field is described by V = 2i + yz2tj −z3t3k, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is the flow incompressible or compressible? (d) Find the z-component of the acceleration vector.arrow_forwardThis problem will show you how to obtain the pathline and the streamline for a velocity field. A velocity field is given by u=(ax_1 t)i −(bx_2)j , where a=0.1^s−2 and b=1s^−1. (a) For the particle that passes through the point (x1,x2) = (1,1) at instant t = 0, get the equation of the pathline during the interval from t = 0 to t = 3s. Plot it roughly by hand(b) Get the equations of the streamlines through the same point at the instants t = 0,1, and 2s. Plot it roughly by handarrow_forwardA steady, incompressible, two-dimensional velocity field is given by V-›= (u, ? ) = (2xy + 1) i-›+ (−y2 − 0.6) j-› where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. The angular velocity of this flow is (a) 0 (b) −2yk-› (c) 2yk-› (d ) −2xk-› (e) −xk-›arrow_forward
- A steady, two-dimensional velocity field in the xy-plane is given by V-›= (a + bx)i-›+ (c + dy)j-›+ 0k-›. (a) What are the primary dimensions (m, L, t, T, . . .) of coefficients a, b, c, and d? (b) What relationship between the coefficients is necessary in order for this flow to be incompressible? (c) What relationship between the coefficients is necessary in order for this flow to be irrotational? (d ) Write the strain rate tensor for this flow. (e) For the simplified case of d = −b, derive an equation for the streamlines of this flow, namely, y = function(x, a, b, c)arrow_forward1. For a velocity field described by V = 2x2i − zyk, is the flow two- or threedimensional? Incompressible? 2. For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0, find the slope of the streamline passing through the point [2, 4] at t = 2. 3. Find the angle the streamline makes with the x-axis at the point [-1, 0.5] for the velocity field described by V = −xyi + 2y2jarrow_forwardA two dimensional velocity field is given =2nx2-yi+(3nxy+x2)j (where n=3439) Is this field steady? Obtain an expression for the material derivative of V.arrow_forward
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