In Fig. 14-49, water flows through a horizontal pipe and...

In Fig. $14-49,$ water flows through a horizontal pipe and then out into the atmosphere at a speed $v_{1}=15$ $\mathrm{m} / \mathrm{s} .$ The diameters of the left and right sections of the pipe are 5.0 $\mathrm{cm}$ and 3.0 $\mathrm{cm} .$ (a) What volume of water flows into the atmosphere during a 10 $\mathrm{min}$ period? In the left section of the pipe, what are $(\mathrm{b})$ the speed $v_{2}$ and (c) the gauge pressure?

In Fig. $14-49,$ water flows through a horizontal pipe and then out
into the atmosphere at a speed $v_{1}=15$
$\mathrm{m} / \mathrm{s} .$ The diameters of the left and right sections of the pipe are 5.0 $\mathrm{cm}$ and 3.0
$\mathrm{cm} .$ (a) What volume of water flows into the atmosphere during a 10 $\mathrm{min}$ period? In the left section of the
pipe, what are $(\mathrm{b})$ the speed $v_{2}$ and (c) the gauge pressure?

Key Concepts

Continuity Equation

This concept states that for steady, incompressible fluid flow, the mass flow rate must remain constant throughout the pipe. In practical terms, the product of cross-sectional area and fluid velocity is constant at every point along the flow, meaning that a change in area will result in a corresponding change in velocity.

Bernoulli's Equation

This principle relates the pressure, velocity, and elevation in a flowing fluid, stating that the sum of the pressure energy, kinetic energy per unit volume, and potential energy per unit volume remains constant along a streamline. It is fundamental in predicting changes in fluid pressure when the velocity changes in a pipe.

Volumetric Flow Rate

Volumetric flow rate is the volume of fluid flowing per unit time and is calculated by multiplying the cross-sectional area of the pipe by the velocity of the fluid. This concept is essential in determining the total volume of fluid exiting or entering a system over a period of time.

Gauge Pressure

Gauge pressure is the pressure of a fluid relative to the ambient atmospheric pressure. It is used to assess the pressure differences within a system where the external atmospheric pressure is considered as the reference, and is especially important in understanding the forces driving fluid motion in a system where openings to the atmosphere occur.

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