The Levitating Water Bridge · AI Generator #GEN-FD67B19C
Physics · fluid-mechanics
Problem
A remarkable phenomenon occurs when two beakers of pure water are brought close together with a high voltage applied between them: a stable water bridge forms that appears to defy gravity. In a laboratory demonstration, two cylindrical beakers each with radius R=2.0cm are positioned so their rims are separated by a horizontal gap of d=5.0mm. When a voltage of V=15kV is applied between the beakers (making them electrodes), a water bridge with circular cross-section forms.
The bridge is held together by electrohydrodynamic forces, but water must flow through it to maintain the structure. Measurements show that the bridge has a radius of r=1.5mm and the water flow rate through the bridge is Q=2.0mL/min. The electrical field creates a pressure difference that drives this flow, while surface tension provides the radial confinement.
(a) Calculate the flow velocity of water through the bridge.
(b) Using Poiseuille's law for laminar flow through a cylindrical tube, determine the effective pressure difference driving the flow. The dynamic viscosity of water is η=1.0×10−3Pa⋅s.
(c) The electrohydrodynamic pressure difference is given by ΔP=21ε0E2, where E is the electric field strength and ε0=8.85×10−12F/m. Assuming the electric field is approximately uniform across the bridge, calculate the electric field strength and compare it to the applied field Eapplied=V/d.