In a papermaking or like operation wherein fibers are supplied to a headbox in a foamed furnish, a method of controlling furnish flow including the steps of controllably advancing the furnish along a flow path to the headbox, measuring the volume flow rate of furnish through a fixed cross-sectional area in the path with a magnetic flowmeter, combining the flow rate measurement at least with measured values of furnish density and pressure in the path and with a reference pressure value to obtain a corrected volume flow rate value, and controlling the advance of furnish in the path upon departure of this corrected value from a desired value so as to change the corrected value toward the desired value. A temperature measurement can also be combined with the other measured values, and with a reference temperature value, in obtaining the corrected flow rate value. If the headbox has a variable slice opening, a measured value of slice opening dimension can be combined with the corrected volume flow rate value to ascertain the discharge velocity of the furnish issuing from the headbox, and the control of furnish advance can be made responsive to departure of this ascertained velocity from a desired value so as to charge the ascertained velocity toward the desired value. The method can be practiced to control plural furnish flows supplied to a multichannel headbox, with the corrected flow rate values of the individual flows being summed to obtain a total flow rate or ascertained velocity value for control of overall flow conditions. Apparatus for controlling a flow or flows of foamed furnish includes a magnetic flowmeter, devices for making and transmitting measurements of at least furnish density and pressure, a control unit for receiving and combining the measurements thus made by the flowmeter and the other devices, and furnish flow control means such as a variable speed pump controlled by signals from a control unit.