In wireless sensor networks, nodes commonly have limited energy and communication ability. Desiging efficient protocols and algorithms to complete various tasks efficiently with limited resources has become a challenge in wireless sensor networks. Considering the receiver capacity and mixed traffic in wireless sensor networks, this paper investigate the utility fair flow control problem with joint power and receiver capacity constraints. Since conventional dual decomposition algorithms often have drawbacks such as slow convergence, difficult adjustment of stepsize and large communication overhead, this paper proposes an event-triggered distributed algorithm for the flow control problem studied in this paper. Both theoretical analysis and simulation results show that the average broadcast period of sensor nodes when using event triggered distributed algorithm is longer than that of dual decomposition. Compared with the dual decomposition algorithm, this event triggered distributed algorithm reduces the amount of information exchange among nodes, decreases the communication overhead in wireless sensor networks greatly. The simulation results also show that the event triggered distributed algorithm has a much faster convergence than the dual decomposition algorithm and the former has better scalability to the network size. Additionally, compared with the conventional rate fair flow control mechanism, the utility fair flow control model can better cater for the networks scene with a mix of elastic and inelastic traffic.