Calculating The Cavitation Number:
The Cavitation Number or Sigma = (Pa + Pd − Pv) / (½ρVa2)
Pa = atmospheric pressure in pounds per square foot =
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:
The Table has been converted to psf from the original
||Vapor Pressure FW
||Vapor Pressure SW
Va = inflow velocity to the propeller, ft/sec
ρ = water density,
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
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