An apparatus and method are disclosed wherein at least one parameter associated with a core-annular flow (CAF) in a pipe is measured by sensing unsteady pressures associated with undulations formed at the interface of a core region and an annular region in the CAF at different axial locations along the pipe. The at least one parameter, which may include a flow velocity of the CAF, Mach number associated with the CAF, and a volumetric flow rate of the CAF, is determined using sensed unsteady pressures. The CAF may be developed from a shear thinning fluid, such as bitumen froth or from a wood pulp fiber suspension. Alternatively, the CAF may be developed from a lubricating fluid, such as water, and a fluid to be transported, such as oil, where the fluid to be transported forms the core region and the lubricating fluid forms the annular region.