Vehicular ad hoc networks (VANETs) are expected to play an important role in our lives. They will improve traffic safety and bring a revolution on the driving experience. However, these benefits are counterbalanced by possible attacks that threaten not only the vehicle's security, but also passengers lives. One of the most common ones is the Sybil attack, which is more dangerous than others since it could be the starting point of many other attacks in VANETs. This paper proposes a distributed approach allowing the detection of Sybil attacks using the traffic flow theory. The key idea here is that each vehicle will monitor its neighbourhood in order to detect an eventual Sybil attack. This is achieved by comparing between the real accurate speed of the vehicle and the one estimated using the V2V communications with vehicles in the vicinity. This estimated speed is obtained using the traffic flow fundamental diagram of the road's portion where the vehicles are moving. A mathematical model that evaluates the rate of Sybil attack detection according to the traffic density is proposed. Then, this model is validated through some extensive simulations conducted using the well-known NS3 network simulator together with SUMO traffic simulator.