An Eulerian velocity vector field is described by V = 3xzj + yk, where i, j and k are unit vectors in the x-, y- and z-directions, respectively. (a) Is the flow one-, two- or three-dimensional? (b) Is the flow compressible or incompressible? (c) What is the acceleration following a fluid particle? (d) If gravity and viscous forces can be neglected, what is the pressure gradient?

Q: Consider the following steady, three-dimensional veloc ity field in Cartesian coordinates: V-› = (u,…

A: Any given flow is incompressible if the divergence of its velocity field is zero.

Q: A velocity field is described (in Cartesian coordinates) by u = 2−x3/3, v = x2y−zt, w =…

A: solution given u=2-x3/3  ,  v=x2y-zt  ,  w=0(a)  ay=∂v∂xu+∂v∂yv+∂v∂zw+∂v∂t

Q: 1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel…

A:

Q: two-dimensional incompressible flow are: The velocity components in a 8 u=8x²y-y² and v=- - 8xy + 3…

A:

Q: Verify whether or not the following difference representation for the continuity equation for a 2-D…

A:

Q: 1. Which of the following functions could represent the velocity potential for the two- dimensional…

A:

Q: Derive an equation for volumetric strain rate and use it to verify that the following velocity field…

A: Given velocity field  V = (uo+bx)i-byj Find the volumetric strain rate and verify that its…

Q: Q2\ In one dimensional f low, the velocity at a point be given in the Eulerian system by u= x+t.…

A: 1-D velocity u = x+t 1) a= ? b) x= ?

Q: 4. Consider a velocity field V = K(yi + xk) where K is a constant. The vorticity, Qz , is (A) -K (B)…

A: Option a is correct.

Q: Consider the following steady, two-dimensional, incompressible velocity field: V = (u,v) = (3ax²)ï +…

A:

Q: An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are…

A:

Q: "A steady, incompressible, two-dimensional velocity field is given by V = (u, v) = (2.7-1.75x, 0.7+…

A:

Q: 1) If for a flow a stream function exists and satisfies the Laplace equation, then which of the…

A: 1] If velocity potential function exists then flow will be irrotational flow. ... If stream function…

Q: (d) Consider the following steady, three dimensional velocity field in Cartesian coordinates. V =…

A:

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.