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.

Solutions

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 1 year ago

Next > < Previous

Related Solutions

2. Assume that the potential in Cartesian coordinates is given as V=x2-y2. According to this; (a)...

2. Assume that the potential in Cartesian coordinates is given as V=x2-y2. According to this; (a) The value of the potential at coordinate P (2, -1,3) (b) Electric field, the magnitude of the displacement vector and field lines (c) Calculate the charge density on the conductive surface

The Cartesian coordinates of a point are given. (a) (2, −5) (i) Find polar coordinates (r,...

The Cartesian coordinates of a point are given. (a) (2, −5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = (b) (-2, −2) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) =...

The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ)...

The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = b. (5,5sqrt(3)) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find...

a) Given a vector field Ã = zỹ +(3y + 2)2 î in cartesian coordinates, determine...

a) Given a vector field Ã = zỹ +(3y + 2)2 î in cartesian coordinates, determine whether it is solenoidal (V · À = 0), conservative (D x X = 0) I Div x A (Cylinderical Coordinates) ii) Calculate integral A*dl , where the contour C is the unit circle (r=1) traversed in anticlockwise direction

Consider an incompressible flow in cylindrical coordinates with velocity field v = Cr^(a) θ^ where C...

Consider an incompressible flow in cylindrical coordinates with velocity field v = Cr^(a) θ^ where C is a constant (a) Show that the flow satisfies the Navier-Stokes equations for only two values of a. (b) Given that p(r; θ; z) = p(r) only, and neglecting gravity, find the pressure distribution for each case, assuming that the pressure at r = R is p0

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point...

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point b. (2, π/4) c.(−3, −π/6)

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar...

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar coordinates (r, θ) of the point so that r > 0 and 0 ≤ θ ≤ 2π. (b). The polar coordinates (r, θ) = (−3, 5π/6) of a point are given. Find the Cartesian coordinates (x, y) of this point.

A velocity vector field is given by F (x, y) = - i + xj a)...

A velocity vector field is given by F (x, y) = - i + xj a) Draw this vector field. b) Find parametric equations that describe the current lines in this field. c) Obtain the current line which passes through point (2,0) at time t = 0 and represent it graphically. d) Obtain the representation y = f(x) of the current line in part c).

Given the following set of coordinates on a Cartesian plane: {(1,1), (2,2), (3,2.5), (4,3)} Find the...

Given the following set of coordinates on a Cartesian plane: {(1,1), (2,2), (3,2.5), (4,3)} Find the quadratic function (polynomial of the second degree) that best fits the data set. Solve this problem using the orthogonality resources and present a “step by step” solution. Sketch the points and the curve.

A two-dimensional transient velocity field is given by u = ax(b + ct) v = ey(f+...

A two-dimensional transient velocity field is given by u = ax(b + ct) v = ey(f+ ht) where u is the x velocity component and v, the y component. Find: The trajectory x(t), y(t) if x = x0, y = y0 at t = 0. The streamline that passes through x0, y0 when t=0 and plot it. The acceleration field. a (-) = 5 b (1/s) = 5 c (m) = -1 e (-) = 5 f (1/s) = 5...

Subjects