The velocity components in 3-dimensional flow is given by u = 4x³; v = –10x²y and w = 2t. The resultant velocity at a point (1, 1, 1) and at t = 1 will be
- A√100 units
- B√105 units
- C√110 units
- D√120 unitsCorrect
Solution
Concept
Resultant velocity in 3D flow
Formula
V = √(u² + v² + w²)
Step-by-step solution
1. At (1, 1, 1): u = 4x³ = 4. 2. v = −10x²y = −10. 3. w = 2t = 2 (t = 1). 4. V = √(16 + 100 + 4) = √120 units.
Explanation
Substitute the point and time into each component and combine them as the square root of the sum of squares.
Shortcut
16 + 100 + 4 = 120.
Common mistake
Forgetting the time-dependent component w.
Correct answer: D) √120 units