Electromagnetic Induction | IPhO 2001 | Pathfinder Solutions | Magneto-Hydrodynamic (MHD) Generator скачать в хорошем качестве

Electromagnetic Induction | IPhO 2001 | Pathfinder Solutions | Magneto-Hydrodynamic (MHD) Generator

#pathfinderphysics #ipho #olympiads #JEEAdvanced2001 IPHO 2001 MAGNETOHYDRODYNAMIC (MHD) GENERATOR A horizontal rectangular plastic pipe of width w and height h, which closes upon itself, is filled with mercury of resistivity ρ. An overpressure P is produced by a turbine which drives this fluid with a constant speed v0. The two opposite vertical walls of a section of the pipe with length L are made of copper The motion of a real fluid is very complex. To simplify the situation we assume the following: • Although the fluid is viscous, its speed is uniform over the entire cross section. • The speed of the fluid is always proportional to the net external force acting upon it. • The fluid is incompressible These walls are electrically shorted externally and a uniform, magnetic field B is applied vertically upward only in this section a) Find the force acting on the fluid due to the magnetic field (in terms of L, B, h, w, ρ and the new velocity v) [2.0 pts] b) Derive an expression for the new speed v of the fluid (in terms of v0, P, L, B and ρ ) after the magnetic field is applied. [3.0 pts] c) Derive an expression for the additional power that must be supplied by the turbine to increase the speed to its original value v0. PATHFINDER EMI BUILD YOUR UNDERSTANDING Q3 The basic principle of magneto hydrodynamic generator used for generating electricity is described here by a simple model