Exact solutions to some axisymmetric problems in magnetohydrodynamics

Steady-state axisymmetric flow of an incompressible perfectly conducting fluid is analyzed with allowance for the circular motion and the azimuthal component of the magnetic field. In the case of a nonviscous fluid, an equation of motion integral is obtained which relates the Bernoulli function to the azimuthal component of the velocity and magnetic fields. For the case of the rotation of a viscous fluid as a solid, the Bernoulli integral depends on the stream function, Reynolds and Alfven numbers, and the twisting parameter.