A nozzle increases the fluid velocity by tapering inward, whereas a diffuser decreases it by tapering outward. Figure P12.3 shows a rounded nozzle followed by a diffuser whose diameter varies from D₁ to D₂ over a length L. Suppose this combination is installed in the wall of a large, open tank at a depth H below the water level. Although it might seem that adding any tube (tapered or not) to a nozzle would reduce the flow by increasing the resistance, the ability of such an arrangement to increase the flow was known even in ancient Rome.

(a) Explain qualitatively why, under near-inviscid conditions, adding the diffuser will increase the volume flow rate.

(b) Derive an expression to predict the flow rate with the diffuser relative to that with the nozzle alone. Let K_e and K_d be the loss coefficients for the rounded entrance and diffuser, respectively.

(c) For D₂ = 2D₁ and L = 5D₁, data plotted in Blevins (2003, p. 153) indicate that K_d = 0.32. What then would be the percentage increase in flow rate due to the diffuser?

Transcribed Image Text:

Water Tank D₁ L D₂ 2 Figure P12.3 Nozzle-diffuser combination at an opening in a water tank. Air Po