Air conditioning on a university campus is provided by...

Air conditioning on a university campus is provided by chilled water $\left(10^{\circ} \mathrm{C}\right)$ pumped through a main supply pipe. The pipe makes a loop $5 \mathrm{km}$ in length. The pipe diameter is $0.75 \mathrm{m}$ and the material is steel. The maximum design volume flow rate is $0.65 \mathrm{m}^{3} / \mathrm{s}$. The circulating pump is driven by an electric motor. The efficiencies of pump and motor are $\eta_{p}=85$ percent and $\eta_{m}=85$ percent, respectively. Electricity $\cos t$ is $14 \& /(\mathrm{kW} \cdot \mathrm{hr}) .$ Determine (a) the pressure drop, (b) the rate of energy addition to the water, and (c) the daily cost of electrical energy for pumping.

Key Concepts

Pipe Flow Friction Losses

This concept deals with the pressure drop that occurs when fluid flows through a pipe due to friction with the pipe walls. It is typically analyzed using the Darcy?Weisbach equation, where the friction factor (often determined using the Reynolds number and pipe roughness) and the pipe dimensions (length and diameter) play key roles in quantifying the head loss. Understanding friction losses is essential for designing efficient fluid transport systems and selecting components such as pumps.

Energy Transfer in Fluid Flow

This concept pertains to the calculation of the rate at which energy is imparted to a fluid by a pump. It involves determining the hydraulic power requirement based on the product of the pressure increase (or drop, when considered in terms of losses) and the volumetric flow rate. This analysis is fundamental in assessing how much energy must be added to overcome losses in the system and maintain the desired fluid flow.

Pump and Motor Efficiency

This concept involves the consideration of energy conversion losses that occur when electrical energy is converted into mechanical energy (via the motor) and then into fluid energy (via the pump). When calculating the total energy input required from electricity, one must account for these efficiencies, as the actual power consumed will be higher than the hydraulic power delivered to the fluid due to these inherent losses.

Cost Analysis of Electrical Energy

This concept is centered on estimating the operational cost of a pumping system by combining the calculated electrical power consumption (adjusted for pump and motor efficiencies) with the cost of electricity per unit of energy. By integrating the energy usage over time, such as on a daily basis, one can derive the overall cost implications of running the system, an essential aspect for economic and energy management in engineering projects.

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