158 EFFLUX FROM A VESSEL IX MOTtOtf. 



Therefore the whole time of emptying the vessel 

 15-nl tan 8 a Vh 



see'a 

 (See Eland's Hydrostatics, p. 185.) 



88. Efflux from a Tessel in Motion. If the vessel 

 ABCD be filled with liquid to AB, and raised vertically, 

 with an accelerated motion, by a 

 weight P attached to an inextensible 

 string, without weight, passing over 

 two smooth pulleys F, E, the veloc- 

 ity of efflux is augmented ; and if it 

 descends with an accelerated motion, 

 the velocity is diminished. 



Let Q be the weight of the vessel 

 and liquid contained in it. Since 

 the pulleys are perfectly smooth, the 

 tension of the string is the same 

 throughout ; hence the force which causes the motion is 

 the difference between the weights P and Q. The moving 

 force, therefore, is P Q ; but the weight of the mass 

 moved is P + Q. Hence, from (1) of Art. 25, Anal. 

 Mechs., we have 



Q 



(1) 



which is the vertical force of acceleration. Since this force 

 acts vertically upwards on the vessel, and the force of grav- 

 ity g acts vertically downwards, every particle of the liquid 

 presses against the bottom of the vessel, not only with its 

 own weight Mg, but also with its inertia M/. Hence the 



