Reference no: EM133029973

FLUID MECHANICS HOMEWORK

1. The velocity field of a flow is given V = 2x²ti^→ + [4 y(t - 1) + 2x²t ? j^_ m /s, where x and y are in meters and t is seconds. For fluid particles on the x axis, determine the speed and direction of flow.

2. The x and y components of a velocity field are given by u=x-y and v=x2y-8. Determine the location of any stagnation points in the flow field. That is, at what point(s) is the velocity zero?

3. Show that the streamlines for a flow whose velocity components are u=c(x2-y2) and v=-2cxy, where c is a constant, are given by the equation x2y-y3/3=constant. At which point (points) is the flow parallel to the y axis? At which point (points) is the fluid stationary?

3.4 a) A velocity field is given by u=cx2 and v=cy2, where c is a constant. Determine x and y components of the acceleration. At what point (points) in the flow field is the acceleration zero?
b) A three-dimensional velocity field is given by u=2x, v=-y, and w=z . Determine the acceleration vector.

3.5) Water flows through the curved hose shown in figure below with an increasing speed of V= 10t m/s, where t is in seconds. For t =2 s determine:

a) the component of acceleration along the streamline.

b) the net acceleration (magnitude and direction).