With the valve closed, water flows from tank A to tank B as...

With the valve closed, water flows from tank $A$ to tank $B$ as shown in Fig. P8.112. What is the flowrate into tank $B$ when the valve is opened to allow water to flow into tank $C$ also? Neglect all minor losses and assume that the friction factor is 0.02 for all pipes.

Key Concepts

Flow Distribution in Pipe Networks

In systems where multiple outlets or parallel paths exist, the total flow is divided among the different branches according to the resistance each branch offers. Understanding flow distribution is critical when a change in system configuration, such as opening an additional outlet or valve, alters the flow pathways and pressure drops across the network.

Darcy-Weisbach Equation

This is a fundamental relation in fluid mechanics which relates the head loss due to friction in a pipe to the flow velocity, pipe length, pipe diameter, and the friction factor. It shows that for a given flow rate, longer or narrower pipes cause more head loss, and it is crucial for calculating pressure drops in pipe networks.

Friction Factor

The friction factor quantifies the resistance to flow due to friction along the internal surface of the pipes. It is used in the Darcy-Weisbach equation and depends on the pipe roughness, flow regime, and hydraulic diameter. A specified friction factor simplifies the analysis by providing a constant measure of friction loss in all pipes in a system.

Head Loss

Head loss represents the energy loss per unit weight of fluid due to friction and other dissipative effects as the fluid flows through a conduit. In piping systems, head loss calculations are essential to determine the available pressure and driving force for fluid flow, influencing the design and operation of the network.

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