Problem 2: Determination of Flux using Surface IntegrationA surface of x? + y = 4 for z =[0,3] is under a vector field F(x, y, z) = 4x i + 2y?j + z? k.(a) Graph the surface and the vector field.(b) Determine the flux across the surface.

Given: Surface x2+y2=4 for z∈0,3. Vector field Fx,y,z=4xi+2y2j+z2k. To do: Graph the surface and…

Answered: Problem 2: Determination of Flux using…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

See similar textbooks

Similar questions

Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.
Find the counterclockwise circulation and the outward flux of the field F = (-sin y)i + (x cos y)j around and over the square cut from the first quadrant by the lines x = pai/2 and y = pai/2.
7. Find the circulation of the field F(x, y) = xi+yj around the circle r(t) =(cost)i + ( sin t)j: 8. Find the flow of the velocity field F(x, y) = (x + y)i-(x2+y2)j alongeach of the following paths from (1, 0) to (-1, 0) in the xy-plane ne.a)The upper half of the circle x2+y2=1b) line segment from (1, 0) to (-1,0)
calc 3 13.7 #5 Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx kS is the part of the paraboloid z = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation.
The flow of a gas with a density of d = 0.3 kg/m2 987 over the closed curve r(t) = (cos t)i + (sin t)j, 0<= t <= 2pai, is given by the vector field F = dv, where v = x2i - yj is a velocity field measured in meters per second. Find the flux of F across the curve r(t).
1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line through the origin.
An Eulerian flow field is described in Cartesian coordinates by V = 4i+xzj+5y3tk. (a) Is it compressible? (b) Is it steady? (c) Is the flow one-, two- or three-dimensional? (d) Find the y-component of the acceleration. (e) Find the y-component of the pressure gradient if the fluid is inviscid and gravity can be neglected.
The flow of a gas with a density of δ = 0.001 kg/m2 over the closed curve r(t) = (-sin t)i + (cos t)j, 0 ≤ t ≤ 2p, is given by the vector field F = δv, where v = xi + y2j is a velocity field measured in meters per second. Find the flux of F across the curve r(t).
Find the flux of the fields F1 = 2x i - 3y j and F2 = 2x i + (x - y)j across the circle r(t) = (a cos t)i + (a sin t)j, 0<= t <=2pai.
1. (Section 17.7) Use Stokes’ Theorem to calculate the work done by −→F (x, y, z) = ex2ˆı − 2xzˆj + xˆk in moving a particle aroundthe closed path determined by the intersection of positively oriented surface S : x + 4y + 2z = 4 and the coordinate planes.
A path C is defined by the parametric equations: x (t) = t, y (t) = t2, 0 ≤ t ≤ 1, and a vector field is defined by the equation F = y2i + xj What is the value of the line integral ∫C F • ds
calc 3 13.7 #6 Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + x j + z2 kS is the helicoid (with upward orientation) with vector equation r(u, v) = ucos(v)i + usin(v)j + v k, 0 ≤ u ≤ 5, 0 ≤ v ≤ 2?.

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Problem 2: Determination of Flux using Surface Integration A surface of x? + y? = 4 for z = [0, 3] is under a vector field F(x, y, z) = 4x i + 2y2 j+ z? . (a) Graph the surface and the vector field. (b) Determine the flux across the surface.