Blockchain, a vital technology in today’s era, changed the way we share, manage and exchange our data in a centralized way to decentralized architecture. With the increasing demand for Blockchain, various platforms are available to implement public, private, consortium, or permissioned, permissionless Blockchain. Hyperledger, an open-source, permissioned, distributed ledger-based Blockchain, was hosted by Linux. This paper explores Hyperledger Fabric Private Blockchain Network (HFPBN). The architecture of HFPBN with its components and transaction flow is explored in detail. The Blockchain in HFPBN comprises multiple blocks that are linked to each other. The block elements are discussed in detail with their type and size, and after that, the total size of the block depending upon various parameters is calculated. Further, one application of Blockchain, i.e., Vehicular Ad-hoc Networks (VANETs), is discussed in this paper as a case study. The VANET application is being implemented on the Hyperledger Fabric platform. Formulas showing the dependency of various parameters like endorsement policy, number of transactions, and number of reads and writes on block size are derived and shown in their relationship through the graph for the VANET system. The impact of block size on various performance parameters like throughput, latency, memory, and CPU utilization for the VANET system is then analyzed using Hyperledger Caliper. An optimal required value of throughput and latency is achieved for Blockchain-based VANET. Also, the Hyperledger Fabric platform seems suitable for many applications as it creates separate Blockchain for different applications.