Q. A hypothetical velocity field is given in Cartesian Coordinates by: V? = 4z^2t i ?...

Q. A hypothetical velocity field is given in Cartesian Coordinates by: V? = 4z^2t i ? 4x k where i, j and k are the unit base vectors. t is the time variable and (x, y, z) are the Cartesian Coordinates in the ( i, j , k ) directions respectively. The fluid density is constant and given by p = 1000kg/m^3

5(a) Give the (x, y, z) components of V? which are written
(u, v, w)respectively. Check whether the flow satisfies the
appropriate continuity equation and conclude whether this
flow is physically possible. Note that the general continuity
equation is given on the formulae sheet at the end exam
paper.

5(b) Give the general expression of the acceleration field from
the above velocity field in the Eulerian frame of reference
and calculate the acceleration at (t, x, y, z) = (t, ?1,5,1) and
at (t, x, y, z) = (1, ?1,5,1) .

5(c) Calculate the component of the velocity in the direction of
the vector t = 2 i + a j, written Vt (where a is an unknown constant) . This can be obtained from:
Vt = V??t/|t |

where the dot indicates the dot product of vectors and the
bold font indicates that we are dealing with vectors.

5(d) Check whether the pressure field p = 2x + y satisfies the
appropriate form of the incompressible x momentum
equation which may be derived from the equation given on
the formulae sheet at end of the examination paper. You
can neglect gravity.

Expert Solution

I couldn’t solve for the 4th question since no paper was provides. And There are so many mistakes in the question. I tried my best to provide answer for each and evary question. Repost the question without any question marks and provide paper insted which will be very much clear

samet mamat answered 2 years ago

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