The Bell and Gossett pump of Prob. P11.8, running under the...

The Bell and Gossett pump of Prob. P11.8, running under the same conditions, delivers water at $20^{\circ} \mathrm{C}$ through a long, smooth, 8 -in-diameter pipe. Neglect minor losses. How long is the pipe?

Key Concepts

Darcy?Weisbach Equation

This fundamental formula in fluid mechanics relates the head loss due to friction in a pipe to the length of the pipe, the diameter, the flow velocity, and the friction factor. It is crucial for analyzing how the energy imparted by a pump is lost along a pipe, thereby helping to determine parameters such as the pipe length required for a given head loss.

Friction Factor

The friction factor is a dimensionless coefficient used in the Darcy?Weisbach equation that quantifies the resistance to flow due to friction along the inner surface of a pipe. Its value depends on the flow regime (laminar or turbulent) and the roughness of the pipe, and it can be determined using the Moody diagram or empirical correlations.

Reynolds Number

The Reynolds number is a dimensionless quantity that indicates whether flow in a pipe is laminar or turbulent by comparing inertial forces to viscous forces. It is essential for choosing the appropriate friction factor correlation and thus directly impacts the calculation of head loss in pipe flow.

Energy Balance in Pump-Pipe Systems

This concept involves equating the energy supplied by the pump to the energy losses in the system due to friction. By matching the pump head (from its performance curve) to the frictional losses (computed via the Darcy?Weisbach equation), one can determine system parameters such as the pipe length required to achieve the desired operating conditions.

Fluid Properties

Knowledge of the fluid properties, such as the density and viscosity of water at a specified temperature (in this case, 20°C), is essential. These properties affect both the Reynolds number and the friction factor, thereby influencing the calculation of head loss in the pipe.

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