The sewer outlets of a house constructed on a slope are 8.16 m below street level. If the sewer

step 1 This problem covers the concept of the hydrostatic pressure. The hydrostatic pressure p2 equals

The sewer outlets of a house constructed on a slope are 8.16...

The sewer outlets of a house constructed on a slope are $8.16 \mathrm{~m}$ below street level. If the sewer is $2.08 \mathrm{~m}$ below street level, find the minimum pressure differential that must be created by the sewage pump to transfer waste of average density $926 \mathrm{~kg} / \mathrm{m}^{3}$

Key Concepts

Gravitational Acceleration

Gravitational acceleration, the acceleration due to Earth's gravity (approximately 9.81 m/s²), is a constant in hydrostatic calculations. It quantifies the influence of gravity on a fluid's pressure distribution and is used to determine the force exerted by the fluid column over a specific elevation difference.

Elevation Difference

Elevation difference is the vertical distance between two points within a fluid system, such as the starting and ending points of fluid discharge. This height difference directly influences the hydrostatic pressure that must be overcome by the pump, making it a fundamental parameter in designing fluid transfer systems.

Fluid Density

Fluid density is the mass per unit volume of a fluid. It plays a key role in hydrostatic calculations since the pressure exerted by a fluid is directly proportional to its density. In scenarios where a pump is used to transport fluid, variations in fluid density can significantly affect the required pressure differential.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest as a result of the gravitational force acting on it. It is calculated by multiplying the fluid's density, gravitational acceleration, and the vertical height of the fluid column. This concept is crucial when determining how much pressure is needed to overcome a given height difference in fluid systems.

Pressure Differential

Pressure differential refers to the difference in pressure between two points in a fluid system. In applications like pumping, it determines the energy required to move the fluid from a lower level to a higher level. This concept is essential for ensuring that the pump creates enough pressure to counteract the hydrostatic pressure due to elevation changes.

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