You recently bought a house and want to improve the flow...

You recently bought a house and want to improve the flow rate of water on your top floor. The poor flow rate is due to three reasons: The city water pressure at the water meter is poor $(p-200 \mathrm{kPa} \text { gage }) ;$ the piping has a small diameter $(D=1.27 \mathrm{cm})$ and has been crudded up, increasing its roughness $(e / D=0.05) ;$ and the top floor of the house is $15 \mathrm{m}$ higher than the water meter. You are considering two options to improve the flow rate: Option 1 is replacing all the piping after the water meter with new smooth piping with a diameter of $1.9 \mathrm{cm} ;$ and option 2 is installing a booster pump while keeping the original pipes. The booster pump has an outlet pressure of 300 kPa. Which option would be more effective? Neglect minor losses.

Key Concepts

Booster Pumps

Booster pumps function by adding extra energy into the fluid, thereby increasing the pressure and assisting the water to overcome frictional losses and static head effects. They are an effective solution when the supply pressure is inadequate, though they often require additional power and maintenance considerations.

Darcy-Weisbach Equation

This fundamental equation in fluid mechanics quantifies the head loss due to friction in a pipe, taking into account factors such as the pipe's roughness, diameter, length, and the fluid's velocity. It provides the theoretical basis for analyzing how changes in pipe condition affect overall system performance.

Improvement Strategies in Water Distribution

There are typically two strategies to improve insufficient water flow: reducing friction losses by replacing existing, aged, or narrow pipes with larger, smoother ones, or injecting additional energy into the system using a booster pump. Each method directly addresses the factors limiting flow rate, such as inadequate pressure, high friction, and elevation differences.

Friction Losses in Piping Systems

Friction losses occur because the movement of fluid is resisted by the pipe walls, and these losses are strongly influenced by the pipe's diameter, roughness, and length. Larger diameters and smoother surfaces lead to lower friction losses, improving the flow rate, while rough, narrow pipes greatly restrict water movement.

Static Head or Elevational Head

Static head refers to the pressure needed to overcome gravitational forces when water is lifted to a higher elevation. The height difference between the water source and the destination creates an additional pressure requirement to ensure adequate flow at the top floor.

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