Fluid flow through pipelines has a huge number of applications. The pipelines design aims to deliver the fluid in a cost-effective manner with the necessary flow rate and required head. The analysis of the network design for the fluid flow is highly important in order to evaluate its performance. The essential and integral part of the network analysis during the motion of fluid through the pipelines is the estimation of head loss which includes the determination of friction factor. The choosing of the appropriate, optimum and economic conduit involves numerous hydraulic computations. The commonly used, well-established methods universally adopted are the Darcy-Weisbach equation and the Hazen-Williams formula for the determination of major friction loss of the fluid flow. A number of approximate explicit equations have been developed based on the friction factor of the Darcy- Weisbach equation. The study involves selecting an appropriate explicit equation for the determination of the Darcy friction factor and estimating the major head loss existing in the newly modeled pipe network for the farm located at Hamelmalo Agricultural College in Eritrea. Eleven different explicit equations were chosen for the determination of friction factor based on different selection criteria, and the pressure loss was determined in each case and was compared with the standard Colebrook-White equation. Statistical methodologies were used to evaluate and obtain the best fit equation for the network.