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Q: 1. Determine the velocity field v so that the surface F(r, y.t) = (y+t)+ (z+t)? - a² = 0 to be a…
A: The given surface is - F(x,y,t) = (y+t)2 + (x+t)2-a2.......(1) The velocity field (V→) components…
Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…
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Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…
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Q: Let v = (a*z, 2 – 2xyz – 3y + x*y, 3z – x*z) be the velocity field of a fluid. Compute the flux of v…
A: Given the vector field v=x2z,2-2xyz-3y+x2y,3z-x2z
Q: 1. Determine the velocity field v so that the surface F(r,y.t) = (y+t)2+ (r+t)2 - a = 0 to be a…
A: Given the surface Fx,y,z=y+t2+x+t2-a2=0
Q: 1. Determine the velocity field v so that the surface F(r, y,t) = (y+t)+ (z+t)? – a? = 0 to be a…
A: Given surface is Fx,y,t=0 where Fx,y,t=y+t2+x+t2-a2 (i) Let v=ui+vj+wk be the velocity…
Q: 1. Determine the velocity field v so that the surface F(r, y, t) (y+t)+ (r +t)2 - a 0 to be a…
A: Solution:
Q: 3. Consider the vector field F = (y, -x, x² + y?). Find the flux of F through S if: 9– x2 – y? above…
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Q: Consider the gradient vector field V = Vg of the function g(x, y) = x² + y² + e*²-y´ cos(2xy).…
A: We will use the Divergence Theorem in 2D to solve the given flux integral.
Q: For the force field F = (2xe¬Y, (2y – x²e¬y)) in some open connected region containing P(1, 0) and…
A: Given that, F=2xe-y, 2y-x2e-y If F is conservative then ∂2F∂x∂y-∂2F∂y∂x=0
Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…
A: Given, F=x+y,x2-yℝ=x,y:y2≤x≤18-y2 By the general theorem circulation, ∮Pdx+Qdy=∬Qx-PydAWhere,…
Q: Let v = (r*z, 3 – 2ryz – 3y + r²y, 3z – 2²z) be the velocity field of a fluid. Compute the flux of v…
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Q: Evaluate the surface integral SSF F · dS for the given vector field F and the oriented surface S. In…
A: Given vector field is F(x,y,z)=xy i+yz j+zx k. To find the flux F across the surface S: Sis the part…
Q: Find the outward flux of the field F = xz i + yz j + k across the surface of the upper cap cut from…
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Q: Consider the surface S given by y=8−x2−z2, y≥0 oriented in the positive direction of the y axis. be…
A: We will find out the required value.
Q: Suppose that S is the boundary surface of the solid region B that is bounded by the paraboloid z =…
A: Given vector field F→x,y,z=2zey+xy2i→+xz2-2zexj→+x2z+2xe-yk→. To find the flux of the vector field…
Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…
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Q: Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In…
A: Compare the given equation with general equation and find the value of P, Q and R.
Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…
A: The given problem is to find the flux od vector field oriented upward unit normal of the vector…
Q: 6) Given a hemisphere bounded by S,: z = /25 – x2 – y? and S2:z = 0.Find the outward flux of the…
A: The flux of a vector-valued function F(x,y,z)=F1i+F2j+F3k over a surface S is defined as ∫SFdS.…
Q: Find the flux of the vector field F(x,y,z) = xi – yj + zk across o, where o is the portion of the…
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Q: Use the Divergence Theorem to calculate the flux SLSF · d§, where F(x,y, z) =
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Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…
A: The given problem is to find the flux of the given vector field over the given portion of cone…
Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…
A: The given problem is to find the flux of the given vector field across the portion of cone and…
Q: Let v = (5, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the…
A: Given, v→=5,y sinz, cosz Flux=∫∫Sv⇀.ds we have divergence theorem, ∫∫Sv⇀.ds=∫∫∫Sdiv v⇀.dv div…
Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…
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Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…
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Q: Evaluate the outward flux of the vector field F = (2x? – 5e" + sin(2²), –4ry + ln(x*), 5z – 3x²y°)…
A: Given
Q: Q2) Find the flux of the vector field F(x,y, z) = (x, y, z) , where the surface S is the portion of…
A: We use divergence theorem.
Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…
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Q: Given the radial field (x, y, z) (x² + y2 + z²)3/2 r|3/2 Find the outward flux across the sphere of…
A: Flux=∫∫sF→.dS=∫∫DFrθ,ϕ.rϕ×rθdA first parametrize the surface of sphere
Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…
A: Counter clockwise circulation on the region R for the vector field F=M,Nis given by…
Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…
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Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…
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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (x,yz) across the…
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Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = J 8 by using…
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Q: Find the surface integral to evaluate the flux of the vector field F=, where S is the surface of the…
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Q: Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²)…
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Q: Let i = (a° cos z, 5 – 3a'y cos z – 3yz? sin æ, 2° sin æ) be the velocity field of a fluid. Compute…
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Q: Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In…
A: Substitute z=2-x2-y2 in r=xi+yj+zk, to represent the surface S in the vector form. Find rx , rx and…
Q: Find the flux of the field F = 4x i + 4y j + 2 k outward (normal away from the z-axis) through the…
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Q: 29. Let K be the part of the cone z = Vx2 + y? between z = 1 and z 3, oriented upward. Let F(x, y,…
A: Flux through the fluid
Q: Evaluate the surface integral ∬SF⋅dS∬SF⋅dS for the given vector field FF and the oriented surface…
A: Here in the given question, find the surface integral of the given vector field and the oriented…
Q: Evaluate the surface integral || F. dS for the given vector field F and the oriented surface S. In…
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Q: Find the work done by the force field F(x,y) = 4yi + 2xj in moving a particle along a circle x2 + y2…
A: We follow
Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…
A: According to question given that F(x,y,z)=xy i + yz j + zx kz=6-x2-y2 that lies above the square…
Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = xy2i + yz2j +…
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Q: Calculate the flux of the vector field F = x²i+ zk across the portion of the plane described as z =…
A: According to our company policy, we are supposed to answer only first question. For the rest please…
Q: Let E = {(x,y, z) | x² + y² < 1 and xy < z < 2} and let S be the boundary of E, oriented outward.…
A: Using Gauss divergence law: ∯SF.dS=∫∫∫V∇·F.dV =∫∫∫V2+3-1.dxdydz…
Q: Evaluate the surface integral F ds for the given vector field F and the oriented surface S. In other…
A: The parametric representation of the surface S is, x=x, y=2cosθ, z=2sinθ, 0≤θ≤π, 0⩽x≤5 Use the…
