Let v = zk be the velocity field (in meters per second) of a fluid in R3. Calculate the flow rate (in cubic meters per second) through the upper hemisphere (z > 0) text{of the sphere} x^{2} + y^{2} + z^{2} = 1.

Alyce Wilkinson 2021-01-08 Answered
Let v = zk be the velocity field (in meters per second) of a fluid in R3. Calculate the flow rate (in cubic meters per second) through the upper hemisphere (z>0) of the sphere x2+y2+z2=1.
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Szeteib
Answered 2021-01-09 Author has 102 answers
Similar to circle sphere is a two dimensional space where the set of points that are at the same distance r from a given point in a three dimensional space. In analytical geometry with a center and radius is the locus of all points is called sphere Given: The upper hemisphere of the sphere is x2+y2+z2=1 Formula used: Volume=(÷F)dv
V=(0,0,z)
÷F=ddx(0)+ddy(0)+ddz(z) On solving the value, ÷F=0+0+1=1
Volume=(÷F)dv Where, dv=43πr3
x2+y2+z2=1=r2 Where, r = 1 43πr3 Substituting the value of r, then the required value is 4π3
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