In the city water tower, water is pumped up to a level 25 m above ground in a pressurized tank

step 1 So we want to find out how much pressure we would need in order to push up more water into this

In the city water tower, water is pumped up to a level 25 m...

In the city water tower, water is pumped up to a level $25 \mathrm{~m}$ above ground in a pressurized tank with air at 125 kPa over the water surface. This is illustrated in Fig. P1.98. Assuming water density of $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and standard gravity, find the pressure required to pump more water in at ground level.

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Key Concepts

Pumping Systems and Pressure Head

In pumping systems, especially those involving vertical displacement of fluids, the pump must provide enough pressure to counteract both the hydrostatic pressure from the fluid’s weight (often described as the pressure head) and any existing pressures within the system. Understanding how to combine the pressure contributions from the fluid’s height and any imposed system pressures is essential for designing and operating effective fluid transport systems.

Gauge Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure rather than absolute zero. Many practical engineering systems, like pressurized tanks or pipelines, use gauge pressure to indicate the amount of overpressure needed to overcome natural atmospheric conditions. This concept helps in determining the additional pressure required when pumping fluids into a pressurized system.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth according to the formula p = ?gh, where ? is the fluid density, g is the gravitational acceleration, and h is the height of the fluid column. This concept is crucial in understanding the pressure differences within any system containing a stationary fluid.

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