Question

A fluid flow is described by velocity field U̅ = 4x²i – 5x²yj + 1k

What is the absolute velocity (in magnitude) at the point (2, 2, 1)?
1. \(\sqrt {1802} \)
2. \(\sqrt {1828} \)
3. \(\sqrt {1840} \)
4. \(\sqrt {1857} \)

Answer 1

Correct Answer - Option 4 : \(\sqrt {1857} \)

U̅ = 4x²i – 5x²yj + 1k

At point (2, 2, 1) : x = 2; y =2; z =1

U̅ = {4 × (2)²}i – {5 × (2)²× 2} j + 1k

U̅ = 16i- 40 j+ k

The magnitude of velocity is given by:

\(u = \sqrt {{{\left( {16} \right)}^2} + \;{{\left( { - 40} \right)}^2} + \;{{\left( 1 \right)}^2}} = \;\sqrt {1857\;} \) m/s

∴ u = \(\sqrt {1857\;} m/s\)