Bubbles tend to form wherever the pressure in a liquid falls below its vapor pressure (P_v), a phenomenon called cavitation. Shock waves created by the rapid collapse of such bubbles can be very damaging to equipment. A system where this might be a concern is shown in Fig. P2.1. To empty a swimming pool for repairs, a pump with a flow rate Q = 3.93 × 10^–3 m³/s is to be connected to 50 m of rubber hose with a diameter of 5 cm. The hose is hydrodynamically smooth. The pump intake will be 3 m above the hose inlet, which will rest on the bottom, and the initial water depth will be 2 m. The water properties are as in Table 1.2.

(a) Calculate |Δ℘| from just inside the hose inlet (position 1) to the pump intake (position 2).

(b) Determine P₂ when the pool is nearly empty, at which time P₁ = 1.01 × 10⁵ Pa. For water at 20 °C, P_V = 2339 Pa. You should find that P_V < P₂ < P₀, where P0 is atmospheric pressure.

(c) How much might Q be increased without risking cavitation? Why, at a given Q, does the risk increase as the water level in the pool goes down?

Transcribed Image Text:

1 m 2 m 2 P Figure P2.1 Pump and hose for emptying a swimming pool (not to scale).