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The use of Internet of Things (IoT) is becoming increasingly common in agribusiness to increase food production capacity for the expanding global population. Recently, low-power wide-area networks (LPWANs) have been used in the development of IoT applications that require low power consumption and low data transmission rates. LoRaWAN is considered the most suitable communication network for LPWANs for IoT applications in smart agriculture. In this paper, we present an in-depth study of the performance of the LoRaWAN communication network in the context of an IoT application for a pilot farm. We consider several scenarios and analyze simulation results by using Network Simulator 3. We then propose a mathematical model that precisely predicts the successful packet delivery rate for this type of network considering the number of nodes and the transmission interval duration. Finally, we validate the results of our model by comparing them with other simulation results under different scenarios.