The velocity components of an incompressible, two-dimensional velocity field are given by the equations u=y^2-x(1+x) v=y(2x+1)...

The velocity components of an incompressible, two-dimensional velocity field are given by the equations u=y^2-x(1+x) v=y(2x+1) (a)Show that the flow satisfies continuity. (b) Determine the corresponding stream function for this flow field. (c) Determine if the flow is irrotational.

Expert Solution

genius_generous answered 2 years ago

The velocity field of a permanent, incompressible and isothermal flow is given by u = a...

The velocity field of a permanent, incompressible and isothermal flow is given by u = a (x^2 - y^2) (1) v = −2axy (2) w = 0 (3) Gravitational acceleration acts on the z axis only. a) Write the Navier-Stokes equations for this flow, canceling the appropriate terms and replacing the non-zero derivatives with their detailed expression. Be sure to indicate clearly your assumptions. (4 points) b) From the result obtained in (a), demonstrate that the pressure field is continuous...

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...

A velocity field is described by the following equations: ?? = 10y/(x^2 +y^2) , ?? =...

A velocity field is described by the following equations: ?? = 10y/(x^2 +y^2) , ?? = -10x/(x^2+y^2) , and w=0 (a) Is this flow compressible or incompressible? (b) Find the pressure gradient. Assume frictionless flow in the z-axis, the density is 1.2 kg/m3 , and the z-axis is aligned with gravity. Also assume the normal and shear effects are negligible.

The streamlines of the velocity field v(x,y,z)=xlnzi+ylnzj+xk have equations:

Let X ∼ Poisson(λ) and Y ∼ U[X, 2X]. Find E(Y ) and V ar(Y ).

Question: The velocity components for a fluid flow are given as follow: z(x-2)2 u = ty...

Question: The velocity components for a fluid flow are given as follow: z(x-2)2 u = ty w = xy (t is time) t+1 a.) Is the flow incompressible or not? b.) How many dimensions does the flow have? c.) Is the flow irrotational or rotational? d.) Find the local acceleration of the flow along x-direction at the points A(x,y,z,t)=A(0,1,1,4); B(x,y,z,t)=B{2,2,1,0)? e.) Find the convective acceleration of the flow along y-direction at the points A(x.y,z,t)=A(0,1,1,4); B(x,y,z,t)=B(2,2,1,0)?

The vector field given by E (x,y,z) = (yz – 2x) x + xz y +...

The vector field given by E (x,y,z) = (yz – 2x) x + xz y + xy z may represent an electrostatic field? Why? If so, finding the potential F a from which E may be obtained.

Velocity field for this system is: V=[X^2-(yz^1/2/t)]i-[zy^3+(x^1/3z^2/t^1/2)j+[-x^1/3t^2/z*y^1/2]k find the components of acceleration for the system.

Velocity field for this system is: V=[X^2-(y*z^1/2/t)]i-[z*y^3+(x^1/3*z^2/t^1/2)j+[-x^1/3*t^2/z*y^1/2]k find the components of acceleration for the system.

Solve x(y^2+U)Ux -y(x^2+U)Uy =(x^2-y^2)U, U(x,-x)=1

a) U = xy b) U = (xy)^1/3 c) U = min(x,y/2) d) U = 2x...

a) U = xy b) U = (xy)^1/3 c) U = min(x,y/2) d) U = 2x + 3y e) U = x^2 y^2 + xy 4. All functions except c) are differentiable. Do these functions exhibit diminishing marginal utility? Are their Marshallian demands downward sloping? What can you infer about the necessity of diminishing marginal utility for downward- sloping demands?

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