The city of Englewood, Colorado, diverts water for municipal...

The city of Englewood, Colorado, diverts water for municipal use from the South Platte River at elevation $1610 \mathrm{m}$ $[54] .$ The water is pumped to storage reservoirs at $1620-\mathrm{m}$ elevation. The inside diameter of the steel water line is 68.5 $\mathrm{cm} ;$ its length is $1770 \mathrm{m} .$ The facility is designed for an initial capacity (flow rate) of $3200 \mathrm{m}^{3} / \mathrm{hr},$ with an ultimate capacity of $3900 \mathrm{m}^{3} / \mathrm{hr} .$ Calculate and plot the system resistance curve. Ignore entrance losses. Specify an appropriate pumping system. Estimate the pumping power required for steady-state operation, at both the initial and ultimate flow rates.

Key Concepts

System Resistance Curve

The system resistance curve represents the relationship between head loss (or pressure drop) and flow rate for a piping system. It is typically obtained by calculating friction losses using empirical relations for turbulent pipe flow and then plotting the head loss against various flow rates. This curve is essential for matching the system's hydraulic demands with pump performance, ensuring the pump provides enough head at the desired flow rate.

Darcy-Weisbach Equation

The Darcy-Weisbach equation is a fundamental relation used in fluid mechanics to calculate the frictional losses in a pipe. It relates head loss to the pipe length, diameter, fluid velocity, and a friction factor that depends on the flow regime and pipe roughness. This equation is key to developing the system resistance curve by quantifying how flow rate affects energy losses in the system.

Pump Selection

Pump selection involves choosing a pump whose performance curve, or pump curve, intersects appropriately with the system resistance curve, ensuring the pump operates efficiently at the desired flow rates and head requirements. This process takes into account both initial and ultimate capacities of the system, as well as practical considerations such as efficiency, reliability, and operational flexibility.

Pumping Power Estimation

Estimating the pumping power required involves calculating the work needed to overcome the elevation difference and friction losses in the piping system at specified flow rates. This is typically done using the hydraulic power calculation, which multiplies the flow rate and the head (converted to energy per unit weight of fluid), while also accounting for the efficiency of the pump. This estimation helps in determining the appropriate motor size and energy consumption for steady?state operation.

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