At the inlet to a constant-diameter section of the Alaskan...

At the inlet to a constant-diameter section of the Alaskan pipeline, the pressure is $8.5 \mathrm{MPa}$ and the elevation is $45 \mathrm{m} ;$ at the outlet the elevation is $115 \mathrm{m}$. The head loss in this section of pipeline is 6.9 kJ/kg, Calculate the outlet pressure.

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Key Concepts

Bernoulli’s Equation with Head Loss

This principle extends the classical Bernoulli equation to include energy losses due to friction or other sources of dissipation. It relates the pressure, velocity, and elevation (or potential energy) at different points in a flow system while accounting for losses expressed as head loss. This concept is crucial when analyzing real fluid systems where energy is not conserved in its mechanical form because of conversion to thermal energy.

Head Loss

Head loss represents the reduction in total hydraulic head due to frictional forces or minor losses in the flow system. It is typically expressed in units of energy per unit weight (such as kJ/kg or meters of fluid head) and must be subtracted from the available energy when applying energy conservation equations. Understanding head loss is essential for accurately determining pressure drops and energy requirements in fluid mechanics problems.

Pressure Head

Pressure head denotes the contribution of the fluid's pressure to its total energy per unit weight. It is expressed as the equivalent height of a fluid column that would generate the same pressure and is a key component in energy balance calculations such as those derived from Bernoulli’s equation. It illustrates how static pressure can be converted into potential energy in a fluid system.

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