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Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = x² + y², z ≤ 81, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = -xi-yj - zk. (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = x² + y², z ≤ 81, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = -xi-yj - zk. (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Subject :- Advance math 

 

Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = x² + y², z ≤ 81, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = −xi – yj – zk. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = > Feedback Express a surface integral as a double integral. Determine the mass of a fluid as a flux. Use the fact that the flux of F across the surface S in the direction of n is given by F.ndS= 2 t •#/12 F(0, d) n(0, p)||r₂ X rø|| do de where n is the outer unit normal vector of S.
Transcribed Image Text:Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = x² + y², z ≤ 81, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = −xi – yj – zk. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = > Feedback Express a surface integral as a double integral. Determine the mass of a fluid as a flux. Use the fact that the flux of F across the surface S in the direction of n is given by F.ndS= 2 t •#/12 F(0, d) n(0, p)||r₂ X rø|| do de where n is the outer unit normal vector of S.
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