Critical velocity is the highest velocity a fluid can attain while still maintaining laminar (streamlined) flow.
Beyond this speed, the flow becomes turbulent. \[ \text{Reynolds number} \, (Re) = \frac{\rho v d}{\eta} \] where \( v \) is the velocity of the fluid. If \( Re \) exceeds a critical value (typically around 2000 for pipe flow), turbulence occurs.
A current element X is connected across an AC source of emf \(V = V_0\ sin\ 2πνt\). It is found that the voltage leads the current in phase by \(\frac{π}{ 2}\) radian. If element X was replaced by element Y, the voltage lags behind the current in phase by \(\frac{π}{ 2}\) radian.
(I) Identify elements X and Y by drawing phasor diagrams.
(II) Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case?