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Consider a velocity field where the x and y components of velocity are given by
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Chapter 2 Solutions
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- An unsteady velocity field V = xy^2ti + zxj −t^3k exists at the 3D plane along a streamline that passes through the point (3,-1,2) at t = 0. Find the equation representing this streamline.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_forwardConsider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). Calculate the equation of the streamline passing through the point (0, 5).arrow_forward
- An unsteady velocity field V = xy'ti + zxj – t°k exists at the 3D plane along a streamline that passes through the point (3,-1,2) at t = 0. Find the equation representing this streamline.arrow_forwardConsider a velocity field where the radial and tangential components of velocity are Vr = 0 and Vθ = cr, respectively, where c is a constant. Obtain the equations of the streamlines.arrow_forwardIn three-dimensional fluid flow, the velocity component an u = * + y z, v = - (xy + yz + zx). Determine the %3D satisfy the continuity equation.arrow_forward
- At t = 0, an unstable velocity field V = xy²ti + zxj – t³k, emerges in the 3D plane as a result of a streamline passing through the points (3, -1, 2). Determine the equation that can act for the streamline.arrow_forwardConsider a velocity field where the x and y components of velocity aregiven by u = cx and v = −cy, where c is a constant. Assuming the velocity field given is pertains to an incompressible flow, calculate the stream function and velocity potential.Using your results, show that lines of constant φ are perpendicular to linesof constant ψ.arrow_forwardConsider a velocity field where the x and y components of velocity are given by u = cx and v = -cy, where c is a constant. Obtain the equations of the streamlines.arrow_forward
- 2. Consider the Eulerian velocity field u(x, t) = y i + (x – sin t) j, where x = x i + yj and t is the time. Please explain how to find an expression for the streamlines that pass through the point (0, yo) for yo ER. Then, find the nonparametric expression for the pathline of the particle that passes through the point (0, 1/2 ) at t = 0, describing the motion.arrow_forwardA fluid has a velocity field defined by u = x + 2y and v = 4 -y. In the domain where x and y vary from -10 to 10, where is there a stagnation point? Units for u and v are in meters/second, and x and y are in meters. Ox = 2 m. y = 1 m x = 2 m, y = 0 No stagnation point exists x = -8 m, y = 4 m Ox = 1 m, y = -1 m QUESTION 6 A one-dimensional flow through a nozzle has a velocity field of u = 3x + 2. What is the acceleration of a fluid particle through the nozzle? Assume u, x and the acceleration are all in consistent units. O 3 du/dt 9x + 6 1.5 x2 + 2x O Oarrow_forwardIn a certain steady, two-dimensional flow field the fluid den- sity varies linearly with respect to the coordinate x; that is, p = Ax where A is a constant. If the x component of velocity u is given by the equation u = y, determine an expression for v.arrow_forward
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