It is a well-known fact that Roman aqueduct customers obtained extra water by attaching a diffuser to their pipe exits. The figure shows a simulation with a smooth inlet pipe, with and without a \(20^{\circ}\) diffuser expanding to a 6 - \(\mathrm{cm}\)-diameter exit. The pipe entrance is sharp-edged. Calculate the flow rate (a) without, and (b) with the diffuser and interpret the results. (c) For the case of a well-rounded entrance, \(K_{\mathrm{ent}}=\) 0.05 , between the reservoir and pipe inlet for the system with a diffuser, how much would the flow rate increase? For water at \(20^{\circ} \mathrm{C}\), take \(ho=998 \mathrm{~kg} / \mathrm{m}^{3}\) and \(\mu=0.001 \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\).

FIGURE P8-153

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Water 3 m D = 4 cm D = 6 cm 2 L=2m 20 Diffuser .