(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
H08.2 (2 points) Given the vector velocity field V(x, y, z, t) = 4t i + xz j + 2ty3 k a) Is this a valid incompressible flow field? b) Is this flow field irrotational?
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2) Let F(x, y, z) = (2exz, 3 sin(xy), x7y2z6). (a) Find the divergence of F. (b)Find the curl of F. -/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
. Consider the following two dimensional velocity field ~v(x, y) = −xy3ˆi + y 4 ˆj. (a) Sketch a figure of the streamlines for this flow field. Include arrows on your streamlines to indicate the direction of the flow. (b) Is this flow field incompressible or compressible? Show all work. (c) Derive an expression for the vorticity vector ~ζ for this flow field. (d) Is this flow field rotational or irrotational? Provide some evidence in support of your answer
6. Find the divergence and the curl of the vector field \(\mathbf{F}(x, y, z)=4 x y^{2} \mathbf{i}+x e^{4 z} \mathbf{j}+x y e^{-4 z} \mathbf{k}\)
The velocity in a certain two-dimensional flow field is given by the equation: ✓ = 2xti – 2 yı where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. (a) Is flow steady or unsteady (b) Determine the expression of acceleration (c) Check if the flow is compressible or incompressible (d) Check if the flow is rotational or irrotational (e) Sketch the streamlines of t= ls on a x-y plane W
Find the divergence and curl of the vector field \(\vec{F}=y^{2} z^{3} \hat{x}+x y \hat{y}+\left(5 z^{2}+y\right) \hat{z}\)
Solve with all the steps please! Calculate the divergence and the curl of the vector field F(x,y,z) = ( x^3y)i + (xy)j + ( 213 )k. (Where Fis a vector and i,j,k stand for the standard unit vectors)
How do I find the curl and divergence of the vector field F(x,y,z) = {1/√(x2+y2+z2)}*(xi +yj+zk) ?
7. Find (a) the curl and (b) the divergence of the vector field F(x, y, z)= e' sin yi+e' cos yj+zk F.de where is the curve of intersection of the plane : = 5 - x and the cylinder rº + y2 = 9. 8. Use Stokes Theorem to evaluate F(x, y, - ) = xyi +2=j+3yk