Show that polar form of equation of continuity for a two dimensional incompressible fluid is av (ru)+- ar If u = -H cos 0 , then find v and the magnitude of the velocity q, where q = (u, v)

Q: x+3x+2x = 2√e¨¬dt Find x(t). Note that x = dx/dt, etc. (b) What is the value of x(t) ast →∞ ?

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Q: For which regions of flow is the Laplace equation ∇-›2? = 0 applicable? (a) Irrotational (b)…

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Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ (a) Find…

A: Given fx,y,z=yz+nx2y+yz3 Substitute n=5 Hence, fx,y,z=yz+5x2y+yz3 (a) We have to find the equation…

Q: Let 2r + 3y –= 5 be the tangent plane to a surface z = f(r,y) at the point (1,1). (a) Find the…

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Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Let f(x, y, z) = x cos z + y sin z and P = (−1, 1, 4). (a) (b) (c) at P. | Find the rate of change…

A: Here given function as fx, y, z=xcosz+ysinz

Q: The several variable function T(x, y, z) = 6x®y+ 4x²y°z – 5xz2 + 50 gives the temperature at a point…

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Q: Calculate the directional derivatives of the function x²y x²+ y? for (x, y) +0 f(x,y) = for (x, y)…

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Q: (NEED TO DERIVE EQUATION NOT JUST WORDS) In cartesian tangent plane coordinates, derive the…

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Q: Verify in cylindrical coordinates that V-(ïv)=(V -ū5+ū -Vỹ

A: Given: ∇.u→v→=∇.u→v→+u→.∇v→

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: g(x,y,z)=x^2+y^2+(z-3)^2

A: For (a), We need to find the equation of the tangent plane to the level set g(x, y, z) = c at the…

Q: b) Explain when an external flow is two-dimensional, three-dimensional, and axisymmetric. What type…

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Q: Consider a differentiable function p(x,y) with the properties below. Use these properties to answer…

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Q: An equation of the tangent plane to the parametrized surface at the point corresponding to u…

A: Given parametrized surface equation is

Q: What are the expressions for the gradient and Laplacian in cylindrical coordinates (z,r,φ)? Simplify…

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Q: Let w = : F(x, y, z)=x² tan(yz) + e³+1 ln(xy) and let P be the point (1, e, 0). (a) Find the rate of…

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Q: b) Explain when an external flow is two-dimensional, three-dimensional, and axisymmetric. What type…

A: To Determine :-  When an external flow is two-dimensional , three- dimensional , and axisymmetric.…

Q: Consider a fully developed two-dimensional channel flow between two infinite parallel plates…

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Q: 5. Express the flowing quantities in rectangular form. a) sec(x + j1) b) cot(+j3) 2

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Q: y(^) – y = sin ht,y(0) = y'(0) = y"(0) = 0,y"'(0) = 1 %3D %3D

A: The given equation is, y4-y=sinh t                  ............1 The given initial condition is,…

Q: 5. Express the flowing quantities in rectangular form. a) sec( + j1) cot(17/12 + j3 cosh(2 + j3) b)…

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Q: Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,4,0) and (0,0,1). A fluid flows…

A: Given, function is, The rate of flow of the tetrahedron can be calculated by the flux. So, the…

Q: Let w = F(x, y, z) = -x² tan(yz) + e²+1 In(ry) and let P be the point (1, e, 0). (a) Find the rate…

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Q: In spherical coordinates, (r, 0, ø), the gradient takes the form 1df 1 ðf Vf (r, 0, ø) : -î + -0 +…

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