Question

Strength Of Materials

A Venturi pump is a constricted tube (cross-sectional areas A, = 6cm? and A, = 2cm? , see Figure) connected to a vertical pipe as shown. Air is blown through the constricted tube in order to lift water ( p = 1000 kg/ m³ ) from a large tank by a height h= Im through the vertical pipe.

(a) If you want to apply Bernoulli's equation, what conditions need to be fulfilled? (5pts)

(b) You want to operate the pump with atmospheric pressure at the inlet ( p, = Po ). What flow r rate Q of air do you have to pump through the Venturi tube to lift the water? Assume all condition for use of Bernoulli’s equation in the tube are fulfilled, and assume you can neglect the static weight of air. Use Puir = 1kg/m² for simplicity. (15pts)

(c) Maintaining p, = Po = 10° pa , you can pump more water by increasing Q , but only until cavitation occurs (the pressure above the water drops to absolute zero). How large is this maximum flow rate Q max ? (10pts)


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