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The velocity field in a fluid medium is given by

\(\vec V = 3x{y^2}\hat i + 2xy\hat j + \left( {2zy + 3t} \right)\hat k\)

Find the magnitudes and direction of translational velocity at (1,2,1) and at time t = 3.


1. 12î + 4ĵ + 13k̂ 
2. 2î + ĵ + 5k̂
3. 3î + 2ĵ + 5k̂
4. -12î + 4ĵ + 13k̂ 

1 Answer

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Best answer
Correct Answer - Option 1 : 12î + 4ĵ + 13k̂ 

Explanation:

Velocity field in a fluid medium

\(\vec V = 3x{y^2}\hat i + 2xy\hat j + \left( {2zy + 3t} \right)\hat k\)

Magnitudes and direction of translational velocity at (1,2,1) and at time t = 3

= (3×1×22) î + (2×1×2) ĵ + (2×1×2 + 3×3) k̂

= 12î + 4ĵ + 13k̂ 

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