A sensor apparatus and method for identifying a restriction in the flowline of a hydrocarbon production system, utilizes an optical fiber or optical fiber cable which is engaged along and preferably spirally wound around and along the flowline. Spaced apart strain gauges which are advantageously in the form of Bragg grating sensors, are engaged with the optical fiber at spaced locations along the flowline. The strain gauges are also engaged with the flowline to measure strain in the flowline. The hoop strain in particular indicates a change in pressure which can be measured by light signals supplied to and received from the optical fiber. Differences in strain along the flowline indicate pressure gradients in the flowline which in turn identify restrictions in the flowline.