Sec. 41.3 



GENERAL LIQUID-FLOW FORMULAS 



V rh Pressure Indicator 



-Pressure at Stagna- 

 tion Point Q 



I Rom P ressure - O.SyoV^ 



Atmospheric plus 

 Hydrostatic Pressure 

 Due to Head h ^^ 

 -f Po,r^ 



■phe 

 Pressure 



Pressure Dio 



Fig. 41. a Schematic Layout and Pressure 



Diagram for Pressure Observation on a 



Ship Rudder 



As applied to the rudder section of Fig. 4LA, and 

 specifically to conditions at the orifice P, the 

 measured pressure at that point is p, with the 

 ship underway at the speed V. Assume that, at 

 rest in fresh water at a temperature of 59 deg F, 

 the submergence h of the orifice is 8 ft, and that 

 the atmospheric pressure Pa at the time is 14.69 

 psi absolute. 



To find the hydrostatic pressure at the orifice, 

 with the ship at rest, it is noted from Table X3.a 

 of Appendix 3 that the weight density w of the 

 fresh water is 62.366 lb per ft^, equivalent to a 

 pressure of 62.366/144 = 0.433 psi. At a depth 

 of 8 ft the corresponding hydrostatic pressure 

 Ph is 8(0.433) = 3.464 psi. The ambient pressure 

 Pa -h Ph = P^ at the orifice is then 14.69 + 

 3.464 = 18.15 psi absolute. 



Assume next that the vessel of Fig. 41.A is 

 underway at a speed of 29 kt, or 48.98 ft per sec. 

 From Table X3.a the mass density p of the fresh 

 water is 1.9384 slugs per ft^. The ram pressure is 

 then 



5 = I y-' = i^^ (48.98)' = 2,325 lb per ft' 



= 16.147 psi, say 16.15 psi. 



A small pressure diaphragm back of the orifice 

 P on the rudder, connected to an indicating 

 mechanism at the top of the rudder stock, 

 shows a pressure drop of 2.12 psi helow atmospheric 

 when running. The negative differential pressure 

 — Ap below the ambient pressure p^ at rest is 

 then -3.464 - 2.12 = -5.58 psi. The absolute 

 pressure at the orifice is 14.69 — 2.12 = 12.57 psi. 

 These values are shown on the pressure diagram 

 2 in the middle of Fig. 41. B. The Euler number 

 E„ or the pressure coefficient at the orifice P, 

 when underway, is 



E„ = 



Ap 



-5.58 

 16.15 



= -0.3455 



If a model of the ship, with a scale ratio of 25 

 and a corresponding speed ratio of 5, were being 

 run in an endeavor to obtain dynamically similar 

 flow, the Euler number E„ would be the same 

 but the ram pressure q would be, as indicated in 

 diagram 3 of Fig. 41. B, 



?Mod' 



" - 2 I 



f j = (gship)/25 

 0.646 psi. 



I Overall Lencjth for Calculating R,-, and F^ of 

 I Rudder as an Independent Bod-^ 



Chord Lenqlh for Rud der as a! Subm e 



1 r 



I I 



Neoative Differential Pressure, p-po^^ -Ap=-5.58 p' 



Observed Pressure at 



Orifice. Absolute 



,o-l2.57 psia p 



Vapor Pressure-^t^ E 



Absolute Zer & — ^^ .^k"' ---.>.■ ^ -.^ ^ _ r —S:-,^ 



llllllllllllllTlTlllllllllllllllllMlllllllhllllllllllNllllll! 



0.25 psi a 



2 



FOR MODEL TotaV"^ T" 



Ram Pressure <\^^ 0.64-6 ps 



Hydrostatic plus AttnospherJc 



Atmos-l pheric- 



T- 



k T~ . ~T^I'*-606 

 0.084 psi "^ psia 



Negative Differentia 



Pressure p-po^ --Ap'-Q223 psi 



15.475 p^tPH + 

 psia 



^Pa^Phhi 



Ordinate for Atmospheric 

 Pressure is Compressed to 

 0.22 of its Proper Heiqhl 

 Compared to Other Ordinates 

 on this Diaqram 



Vapor Pressure^ 



''Absolute Zei 



' A bsolute .Lero ^ X. 



llllllIlllllllllllllllTlTllMlllllllllllllllMlltllllllllllMII 



Fig. 41. B Details and Pressure Diagrams for a 

 Pressure Measurement on a Rudder 



