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GATE ME 2013 | Question: 26

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The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coordinate system having $i$, $j$ and $k$ as unit base vectors.

                                                                   $\iint_{s}^{ }\frac{1}{4}(F.n)dA$

where $S$ is the sphere, $x^2$ + $y^2$ + $z^2$ =$1$ and n is the outward unit normal vector to the sphere. The
value of the surface integral is

  1. $\pi$
  2. $2\pi$
  3. $3\pi/4$
  4. $4\pi$
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