The water supply of a building is fed through a main pipe 6.00 cm in diameter. A 2.00 -cm-diamet

step 1 For this particular problem, we have to use the equation rate. Rate equals A2V2 equals volume di

The water supply of a building is fed through a main pipe...

The water supply of a building is fed through a main pipe $6.00 \mathrm{cm}$ in diameter. A 2.00 -cm-diameter faucet tap, located $2.00 \mathrm{m}$ above the main pipe, is observed to fill a 25.0 -L container in 30.0 s. (a) What is the speed at which the water leaves the faucet? (b) What is the gauge pressure in the $6-\mathrm{cm}$ main pipe? Assume the faucet is the only "leak" in the building.

Key Concepts

Continuity Equation

The continuity equation in fluid dynamics is based on the conservation of mass, stating that the mass flow rate must remain constant along a streamline in a steady, incompressible flow. This means that the product of cross-sectional area and fluid velocity is constant, allowing one to calculate changes in velocity when the diameter or area of the pipe varies.

Volumetric Flow Rate

Volumetric flow rate is the volume of fluid that passes through a given cross-sectional area per unit time. It is calculated by multiplying the cross-sectional area of the pipe by the velocity of the fluid. This concept is key in determining how quickly a container can be filled or emptied.

Bernoulli's Equation

Bernoulli's equation relates the pressure, velocity, and elevation (height) in a flowing fluid, based on the principle of conservation of energy. It explains how an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or potential energy, making it possible to calculate pressure differences in a system with varying heights.

Gauge Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure. It represents the pressure difference between the inside of a system, such as a pipe, and the surrounding environment. This concept is critical when considering pressure forces in fluid dynamics, especially in systems where the fluid is exposed to or vented to the atmosphere.

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