The sewage outlet of a house constructed on a slope is 6.59 mbe low street level. If the sewer i

step 1 For part A of the given problem, the capacitance of a system is given by C is equal to Q divided

The sewage outlet of a house constructed on a slope is 6.59...

The sewage outlet of a house constructed on a slope is 6.59 $\mathrm{mbe}$ low street level. If the sewer is 2.16 $\mathrm{m}$ below street level, find the minimum pressure difference that must be created by the sewage pump to transfer waste of average density 1000.00 $\mathrm{kg} / \mathrm{m}^{3}$ from outlet to sewer. $+70 \mathrm{pC}$ and $-70 \mathrm{pC}$ , which result in a 20 $\mathrm{V}$ potential difference between them. (a) What is the capacitance of the system? (b) If the charges are changed to $+200 \mathrm{pC}$ and $-200 \mathrm{pC}$ what does the capac- itance become? (c) What does the potential difference become?

The sewage outlet of a house constructed on a slope is 6.59 $\mathrm{mbe}$ low street level. If the sewer is 2.16 $\mathrm{m}$ below street level, find the minimum pressure difference that must be created by the sewage pump to
transfer waste of average density 1000.00 $\mathrm{kg} / \mathrm{m}^{3}$ from outlet to sewer.
$+70 \mathrm{pC}$ and $-70 \mathrm{pC}$ , which result in a 20 $\mathrm{V}$ potential difference
between them. (a) What is the capacitance of the system? (b) If the
charges are changed to $+200 \mathrm{pC}$ and $-200 \mathrm{pC}$ what does the capac-
itance become? (c) What does the potential difference become?

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. It is directly proportional to the fluid’s density, gravitational acceleration, and the vertical height (depth) of the fluid column. This concept is fundamental when calculating the pressure difference required to move fluids – such as sewage – against gravity.

Fluid Density and Gravitational Force

The density of a fluid along with the acceleration due to gravity determines the weight per unit volume of the fluid. When transferring fluids from one elevation to another, knowing the fluid density and the vertical displacement allows us to compute the required pressure difference, ensuring that the pump applies enough force to overcome the weight of the fluid column.

Capacitance

Capacitance is a measure of a capacitor’s ability to store electric charge per unit voltage. It is defined by the relationship C = Q/V, where C is the capacitance, Q is the stored charge, and V is the potential difference between the capacitor’s plates. Capacitance depends on the physical characteristics of the system, such as the area of the plates and the distance between them, and is independent of the amount of charge stored as long as the geometry remains unchanged.

Relationship Between Charge, Capacitance, and Voltage

This relationship is encapsulated in the formula Q = CV, indicating that the charge stored on a capacitor is directly proportional to both its capacitance and the applied voltage. When the amount of charge on the capacitor changes while the capacitance is constant, the voltage must adjust accordingly. Conversely, if the voltage is maintained while the charge varies, it suggests a corresponding change in the effective capacitance or a reconfiguration of the system’s electrical parameters.

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