﻿ Calculating The Cavitation Number
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Calculating The Cavitation Number:

The Cavitation Number or Sigma = (Pa + Pd − Pv) / (½ρVa2)

where:

Pa = atmospheric pressure in pounds per square foot = 2116.8 psf

Pd = water pressure at the propeller hub = ρ × g × (Depth to hub in feet) psf

Pv = water vapor pressure, psf

The following Table of vapor pressures is from the U.S. Coast Guard's Crisis Manual web site:
www.chrismanual.com/intro/prop.htm.

The Table has been converted to psf from the original psi

 Deg. F Vapor Pressure FW(psf) Deg. F. Vapor Pressure SW(psf) 32 12.82 30 11.38 40 17.57 40 16.56 50 25.63 50 24.05 60 36.86 60 34.85 70 52.27 70 50.54 80 73.01 80 73.30 90 100.51 90 100.80 100 136.80 100 136.80

Va = inflow velocity to the propeller, ft/sec

ρ = water density, lb-sec2/ft4, also called Rho:  This value can be found by opening the Density Dialog Box in PSModel then entering the water temperature and selecting Salt Water (SW) or Fresh Water (FW).

g = standard acceleration due to gravity = 32.174 ft/sec2

Calculating the Cavitation Number with PSModel:

When entering MPH and RPM data into a Series Dialog Box the Cavitation Number is calculated automatically and is displayed in the grayed Sigma window or control.

If you just need to calculate a Cavitation Number without completely filling in the Series Dialog Box do the following:

1) Open the Gawn Burrill (GBD) Series Dialog Box which has a large range of Cavitation Numbers.

2) Check the MPH/RPM checkbox.

3) Click on the text [Current Rho ...] and set the water density, ρ.

4) Enter Depth of Prop.

5) Enter the Wake Factor.

6) Enter the Boat MPH.

7) Press the Tab Key or click outside the Boat MPH control, which causes PSModel to perform calculations with the last value entered in a control or window.

8) The calculated Cavitation Number appears in the grayed Sigma control window.

Calculating the Cavitation Number by hand:

1) Boat\Propeller information:

Boat speed = 20 MPH = 29.33 ft/sec

Wake Fraction (1 - w) = 0.95

Flow velocity into the propeller, Va = 29.33 × (1 - w) = 27.86 ft/sec

Water temperature and type = 60 Deg. F., Fresh Water (FW)

Depth below surface of the propeller hub = 2.0 ft

2) Water vapor pressure, Pv = 36.86 psf, from Table above

3) Water density, ρ = 1.9384 lb-sec2/ft4, from PSModel's Density Dialog Box

4) Water pressure at propeller hub, Pd =  1.9383 × 32.174 × 2.0 = 124.73 psf

5) Sigma = (Pa + Pd − Pv) / (½ρVa2) = (2116.8 + 124.73 − 36.86) / (0.5 × 1.9383 × 27.862) = 2.93