402 HYDRAULICS AND ITS APPLICATIONS 



increase in the area of the moving stream and a diminution in its 

 velocity will tend to efficiency by reducing shock and kinetic losses. 



While this conclusion is verified in practice, in the case of the paddle 

 whsel and of the hydraulic jet (see Art. 116) practical considerations 

 soon limit the maximum possible area (sooner in the case of the jet than 

 of the paddle wheel). In the case of the screw propeller, moreover, 

 frictional losses rapidly increase with the area of the screw, while an 

 attempt to increase the area by increasing the radius, increases the 

 centrifugal action of the water, and by reducing the pressure near the 

 centre of the propeller, tends to reduce the effective thrust. 



Paddle Wheels. These give excellent results in smooth water, and 

 where the draught and therefore the depth of immersion of the paddles is 

 not likely to vary largely. They are well adapted for river navigation, 

 particularly for shallow draught vessels, but are quite unfitted for use in 

 any ocean-going boat which may be exposed to rough weather, and whose 

 draught may differ by some feet on the outward-bound and homeward- 

 bound journeys. 



If E = mean foot radius, 



N = number of revolutions per second, 



then 2 TT R N = V P = velocity of paddles relative to the ship in feet per 

 second. 



If V s be the absolute velocity of the ship, (V P V 8 ) is termed the slip, 



V V 



or more correctly the apparent slip, and 100 p ? is termed the per- 



Vp 



centage slip. This in general varies from 20 to 30 per cent. The chief 

 losses are due to shock at entrance and exit from the water and are 

 reduced as far as possible by the use of feathering floats arranged so as 

 to enter the water without shock. Where, as is usual, the paddle wheels 

 are placed amidships, the stream -line motion over the run of the ship is 

 greatly affected, at least over those layers between the surface and the 

 bottom of the wheel, and since the relative velocity of flow over this 

 portion of the ship is largely increased, the effect is to augment the 

 resistance as compared with the towing resistance with paddles removed. 



The Screw Propeller is by far the most important of the three types. 

 Its advantages consist in its possibilities of adoption to high speed prime 

 movers ; its depth of immersion, which makes its efficiency largely inde- 

 pendent of a varying draught, and its reduced liabilitv to accident, in 

 virtue of its sheltered position. 



If P = mean pitch of propeller blades, i.e., the distance the boat 

 would travel per revolution if the screw were supposed to rotate in a fixed 



