Consider the flow of water through a clear tube. It is sometimes possible to obs

Question

Consider the flow of water through a clear tube. It is sometimes possible to observe cavitation in the throat created by pinching off the tube to a very small diameter. We assume incompressible flow with negligible gravitational effects and negligible irreversibilities. As the duct cross-sectional area decreases, the velocity increases and the pressure decreases according to:

Where V1 and V2 are the average velocities through cross-sectional areas A1 and A2. Thus, both the maximum velocity and minimum pressure occur at the throat.

If the water is at 20C, the inlet pressure is 20.803 kPa, and the throat diameter is one-twentieth of the inlet diameter, estimate the minimum average inlet velocity at which cavitation is likely to occur in the throat.

Explanation / Answer

Cavitation occurs when fluid pressure is less than its vapor pressure
At 20C vapor pressure = 2.3 kPa
http://www.engineeringtoolbox.com/cavitation-d_407.html

Use = 1000kg/m3

A1V1=A2V2

V2=(d1/d2)2V1 = 400V1

P1-P2 = (V22-V12)/2

(20.803-2.3)*1000=1000((400V1)2-(V1)2)/2

V1= 0.0023 m/s -> minimum velocity needed to create cavitation

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