82 SPECIAL PHYSIOLOGY 



an orifice (or nozzle) in a reservoir is equal to the velocity which 

 would be acquired by a body falling freely through a height equal 

 to the distance between the orifice and the surface of the liquid." 



Make out a table which will show for each of the first five seconds 

 of a falling body the distance traversed (d) ; the velocity (v) ; the 

 total height at the end of each second respectively (h)\ and derive 

 from this table the value of velocity in terms of g (g = acceleration of 

 gravitation, 32 + ft. or 981 cm. per second) and of t (=time in 

 seconds). 



(1) V = gt. 



(2) H = ^. 



Eliminate t from these two equations and express the value of 

 velocity (V) in terms of the acceleration of gravitation (g) and the 

 height (h). 



(3) V = 



How does the velocity vary in terms of height? The velocity 

 varies as the square root of the height. 



(4) V v'H. 



Given the height of the water in the reservoir (h) and the radius 

 of the nozzle (r), to compute the discharge (D). 



(5) D = area X velocity. 



(6) D = Trr 8 X 44.3 j/h"= 44.3 Trr 1 i/h = 139.2 r 2 j/hT 



The discharge will vary as the product of the square of the radius 

 multiplied by the square root of the height. 



(7) DoorVh. 



3. Observations. To test the influence of the radius and the 

 pressure upon the discharge one uses the law (expressed in D oo r 2 1/h). 

 given above. Note that the discharge varies with two different 

 factors. 



It is a fundamental principle governing all experimental work, 

 that, where one is studying a quantity which varies with two or 

 more factors, he makes all but one of the factors constant and allows 

 the quantity in question to be modified by only one variable factor 

 at a time. 



We will, therefore, make the radius constant by using the small 

 nozzle while we observe the discharge as modified by varying height. 



(1) Take the discharge in c.c. through 3-mm. nozzle at h = 36 cm.; 

 h=49 cm.; /t=64 cm.: 



D : d : : i/H : i/hT 



(2) Take the discharge in c.c. through 6-mm. nozzle at h = 36 cm.; 

 h = 49 cm.; /^=64 cm. In these observations maintain a constant 

 height in the reservoir by letting water flow in from the supply tank. 



