This paper proposes the effective data gathering and energy efficient communication scheme for Wireless Sensor Networks employing Unmanned Aerial Vehicle. In this scheme, we minimize the number of redundant sensors communicating with UAV by assigning the sensors inside the coverage area of UAV's beacon signal into different priority groups. Once the priority segments, Circularly Optimized Frame Selection (COFS), are defined, data communication is handled from higher to lower transmission priority frame sequentially. The work presented in the paper is based on multi-hop approach. Therefore, the plausible algorithms employing the scheme COFS are proposed to engage in effective data collection. As a result, both the proposed scheme and algorithms are significant to obtain low energy consumption as well as increase the lifetime of sensors inside the network. The energy consumption model is also presented. This study is confirmed by simulating the WSN-UAV system employing our proposed model.