The unsteady wall shear stress in accelerating and decelerating turbulent flows of water in a smooth pipe was measured using two different approaches simultaneously : a “direct” mechanical approach, and a more conventional “indirect” approach involving measurement of the transient pressure gradient. The measurements covered a Reynolds number range of between 40,000 to 130,000, and values of acceleration parameter (φ) from -2 to 3. The results showed a surprising trend for the unsteady wall friction to increase in decelerating, and decrease in accelerating flows, contradicting all existing observations. It is possible that the phenomenon of relaminarisation occurring during flow acceleration could have accounted for the reduction in wall shear stress. Based on the test measurements, empirical equations for the unsteady friction factor in terms of the acceleration parameter (φ) are derived. Limiting values of (φ) within which the flow may be approximated as being quasi-steady are also proposed.