406 HYDRAULICS AND ITS APPLICATIONS 



Water may be taken into the pumps either through one or more vertical 

 or horizontal pipes at right angles to the axis of the vessel, through pipes 

 facing forwards in the direction of the axis, or through vertical or hori- 

 zontal pipes fitted with a scoop facing in the direction of motion of the 

 vessel. In the latter case the effect is the same as with the inlet pipes facing 

 forwards except that the scoop introduces a slight additional resistance to 

 motion. If h be the depth of the inlet, the head producing flow along 



the inlet pipe is given by h -\- feet in the two latter cases, and by h feet 



if the inlet opens flush with the sides or bottom of the boat, and since in 

 every case the delivery pressure is that corresponding to the depth of 

 immersion of the outlet, less energy is required of the pump per Ib. 

 of water to discharge at a given velocity with the inlet facing forwards 

 than with a plain side or bottom inlet. In any case the total change 

 of momentum per second is the same provided the discharge velocities 

 are the same. 



Variation of Efficiency with Size of Orifices. 



Assuming the energy of propulsion to be given by k u 3 ft. Ibs. per 

 second (p. 404), where k is constant for a given vessel, 



A W 



k u 3 = uv(v u) 



AW A W , 



.'. K IT + U . ~ V- f 2 = 

 9 9 



A W 



or u = ~ 



1 A W j 

 Substituting this value of u in equation (5), we have 



M . 



Efficiency = 



"V 



A W AW 



Multiplying numerator and denominator by 1 + V 1 + - ~ this 



A. rr 



finally gi^e* 



Efficiency = - ; 



BO that the efficiency of propulsion increases as the ratio -j- increases, 



K 



i.e., in the case of any given boat, as the area of the orifices increases. 

 But as the quantity discharged per minute, and also the size of pump 



