If Vs is the velocity of the vector, r is the radius of curvature and ∂Vn/∂t is the local normal acceleration; what is the expression for total normal acceleration of fluid particles ?
- AdVn/dt = Vs² + r ∂Vn/∂t
- BdVn/dt = Vs²/r + ∂Vn/∂tCorrect
- CdVn/dt = r + Vs² ∂Vn/∂t
- DdVn/dt = r/Vs² + ∂Vn/∂t
Solution
Concept
Normal acceleration = convective + local
Formula
an = Vs²/r + ∂Vn/∂t
Step-by-step solution
1. The convective normal (centripetal) acceleration is Vs²/r. 2. The local normal acceleration is ∂Vn/∂t. 3. Total = Vs²/r + ∂Vn/∂t.
Explanation
Acceleration of a fluid particle has a convective part due to motion along the curved path and a local part due to time variation.
Why the other options are wrong
The other options have the wrong dimensions (Vs² added to an acceleration, or r multiplied by an acceleration).
Shortcut
Centripetal acceleration = V²/r.
Common mistake
Multiplying by r.
Correct answer: B) dVn/dt = Vs²/r + ∂Vn/∂t