Project ForgeEngineering Mathematics
Linear Algebra
GATE 2014
Medium
In a steady incompressible flow, the velocity distribution is given by V⃗=3xî−Pyĵ+5zk̂, where V is in m/s and x, y, and z are in m. In order to satisfy the mass conservation, the value of the constant P (in s⁻¹) is _____
8 s⁻¹(± 0.05 accepted)
Explanation
Incompressible flow requires ∇·V⃗=0: ∂(3x)/∂x+∂(−Py)/∂y+∂(5z)/∂z=3−P+5=0, so P=8.
Source: GATE CH 2014 (2014)
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