Let v = zk be the velocity field of a fluid in R^3. Calculate the flow rate through the upper hemisphere (z > 0) of the sphere x^2 + y^2 + z^2 = 1.

midtlinjeg 2021-02-25 Answered

Let v=zk be the velocity field of a fluid in R3. Calculate the flow rate through the upper hemisphere (z>0) of the sphere x2+y2+z2=1.

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Expert Answer

Szeteib
Answered 2021-02-26 Author has 102 answers

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
Substituting the value of r, then the required value is 4π/3
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