6.4 The three components of velocity in a flow field are given by u = x² + v² + z² v = xy + yz + z? w = -3xz =?/2 + 4 - Determine an expression for the rotation vector. Is this an irrotational flow field?

The velocity components in the x and y directions are given by 3 u = Axy3 - x2y, v = xy2 -- The value of a for a possible flow field involving an incompressible fluid is

1 Velocities are measured at different locations using a data logger and the field is given by the technician in the following vector form. Given that. du du ax = +u-+v. +w du du ôt əx ду əz V = 3tî +xzj+t Find the magnitude of velocity and acceleration at point (1,1,1) at time t = 1 second. Write the acceleration vector. If the fluid is incompressible, show that the flow field satisfies the conservation of mass. zj+ty²k m/s Əv dv dv Əv +u- +v +w- at Əx ду əz dw dw dw dw + w a ₂ = +u Ət Əx dy əz +v

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c. For a given velocity field calculate the constants a, b, and c such that the flow field is irrotational. V = (0.657 + 1.73x + 0.948y + az)i + (2.61 + cx + 1.91y + bz)j+(-2.73x - 3.66y – 3.64z)k

Problem 3: Obtaining the stream function from velocity components The steady state, incompressible flow field for two-dimensional flow is given by the following velocity components: V =16y-x and v, =16x + y %3D Determine the equation for the stream function and make sure continuity is satisfied.