The average flow speed in a constant-diameter section of the...

The average flow speed in a constant-diameter section of the Alaskan pipeline is $2.5 \mathrm{m} / \mathrm{s}$. At the inlet, the pressure is $8.25 \mathrm{MPa}$ (gage) and the elevation is $45 \mathrm{m} ;$ at the outlet, the pressure is $350 \mathrm{kPa}(\text { gage })$ and the elevation is $115 \mathrm{m}$. Calculate the head loss in this section of pipeline.

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Key Concepts

Bernoulli's Equation

A fundamental principle in fluid mechanics that relates the pressure, kinetic energy, and potential energy along a streamline. In this context, it is used in its extended form to include head loss due to friction and other dissipative effects in a flowing fluid.

Head Loss

The reduction in the total energy or head of a fluid as it flows through a pipeline, primarily due to friction and turbulence. It is calculated by comparing the energy per unit weight at two different points along the streamline.

Pressure Head

A representation of the energy due to pressure expressed as an equivalent height of fluid. It is obtained by dividing the fluid pressure by the product of fluid density and gravitational acceleration, allowing pressure differences to be compared with elevation differences.

Elevation Head

The component of energy per unit weight attributable to the elevation of a fluid. Differences in elevation affect the gravitational potential energy and are incorporated into the overall energy balance in the flow.

Kinetic Energy Head

The portion of energy per unit weight associated with the velocity of the fluid, typically expressed as v²/(2g). It provides insight into how the velocity of the fluid contributes to the overall energy balance along the streamline.

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