Two equal length, horizontal pipes, one with a diameter of 1...

Two equal length, horizontal pipes, one with a diameter of 1 in., the other with a diameter of 2 in., are made of the same $m$ aterial and carry the same fluid at the same flow rate. Which pipe produces the larger head loss? Justify your answer.

Key Concepts

Head Loss

Head loss refers to the energy loss per unit weight of fluid as it flows through a pipe, largely due to the friction between the fluid and the interior surface of the pipe. It is a key concept in fluid dynamics and is particularly important in the design of piping systems, as excessive head loss can reduce the efficiency of fluid transport.

Darcy-Weisbach Equation

The Darcy-Weisbach equation is a fundamental formula used to quantify head loss due to friction in a pipe. It relates the head loss to the pipe's length, the flow velocity, the friction factor, and the pipe's diameter. This equation helps engineers understand how changes in these variables can impact the overall energy loss in the system.

Flow Velocity and Cross-Sectional Area

For a given constant flow rate, the flow velocity in a pipe is inversely proportional to its cross-sectional area. This means that when fluid is forced through a smaller diameter pipe, the velocity increases. Higher velocity in a confined channel leads to increased frictional effects, which in turn raises the head loss.

Impact of Pipe Diameter on Friction Loss

The diameter of a pipe has a significant effect on the head loss experienced by the fluid. In pipes carrying the same flow rate, a smaller diameter results in a higher flow velocity and a shorter hydraulic radius, both of which contribute to a higher frictional head loss. Thus, among pipes of equal length and same material, the one with the smaller diameter produces a larger head loss.

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