MAGNETOHYDRODYNA MIC METHODS OF MEASURING MASS VELOCITY AND ELECTRICAL CONDUCTIVITY PARAMETERS VARYING ALONG THE DIRECTION OF THE FLOW

1. During the motion of a conducting medium in an external magnetic field an electric field depending on the velocity of the motion is created. If this velocity is constant, it may be determined by measuring the potential difference between two electrodes placed in the flow. When a resistance is connected between the electrodes, the current arising from this potential difference depends on the resistance of the medium between the electrodes and hence on the electrical conductivity of the medium; by measuring the current we may find the electrical conductivity. A theory presented in two earlier expositions [1, 2] related to measurements of velocity in MHD channels, in which allowance was made for the nonuniformity of the magnetic field and the changes taking place in the velocity and electrical conductivity on passing across the channel. Considerable changes may often take place in these quantities on passing along the channel as well. For example, when a detonation wave passes along such a channel, measurements of the eleetrical-condux~tivity and mass-velocitypro files might provide useful information regarding the chemical reactions in the explosive. Changes taking place in the velocity along the direction of motion have been recorded in experiments with shock tubes [3] and high-speed gas flows [4]. However, the possibility that changes in velocity might influence the results of the measurements has never been considered in existing experimental investigations. A solution was given in [2] to the problem of the electric field in a channel of constant electrical conductivity, due to allowance being made for the changes taking place in the velocity on passing along the channel. It would be a very complicated matter to solve the coresponding problem if the electrical conductivity also depended in an arbitrary manner on the longitudinal coordinate. In order to determine the possibility of measuring the electrical-condu ctivity and velocity profiles magnetohydrodyna mically it is unnecessary to obtain an exact solution of this problem. In this paper we shall find the necessary conditions for making such measurements and shall estimate the errors associated with changes in velocity along the channel. 2. We shall consider that the measurements are carried out in an MHD channel of rectangular cross section as indicated in Fig. 1, although all the results will be applicable to channels of arbitrary cross section. The conducting medium moves along the channel, its velocity at a particular instant of time being v = (v(x), 0,0). The uniform external magnetic field H is directed along the z axis (perpendicular to the plane of the figure). The electrical conductivity of the medium is ~ = or(x). The electrode 1 is grounded; electrode 2 is connected to it through a resistance Ro The walls of the channel are insulators. The quantity