Project ForgeEngineering Mathematics
Linear Algebra
GATE 2009
Medium
For an incompressible flow, the x- and y-components of the velocity vector are vx=2(x+y), vy=3(y+z), where x,y,z are in metres and velocities in m/s. Then the z-component of the velocity vector (vz) for the boundary condition vz=0 at z=0 is
- A5z
- −5z
- C2x+3z
- D−2x−3z
Explanation
Incompressible continuity: ∂vx/∂x+∂vy/∂y+∂vz/∂z=0. ∂vx/∂x=2, ∂vy/∂y=3, so ∂vz/∂z=−5. Integrating with vz=0 at z=0 (and no additional x,y-dependent term needed to satisfy the boundary condition for all x,y): vz=−5z.
Source: GATE CH 2009 (2009)
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