Kinetic energy of a fluid flow can be computed by ||Ipv - vďV, where p(z, y, z) and v(z, y, z) are the pointwise fluid density and 6 velocity, respectively. Fluid with uniform density 1 flows in the domain bounded by z? + 2² = 9 and 0 < y s2. The velocity of parabolic flow in the given domain is v(z, y, 2) = (9 – z² – 2²)j. Find the kinetic energy of the fluid flow. Answer:
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Kinetic energy of a fluid flow can be computed by ∭V12ρv⋅vdV, where ρ(x,y,z) and v(x,y,z) are the pointwise fluid density and velocity, respectively. Fluid with uniform density 1 flows in the domain bounded by x2+z2=9 and 0≤y≤6π. The velocity of parabolic flow in the given domain is v(x,y,z)=(9−x2−z2)j⃗ . Find the kinetic energy of the fluid flow.
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