CIRCULATION. 95 



From these equations derive: 



(3) v=^/2gh; (approximately^ 4.3^h). 

 Expressed as a variation the constant may be dis- 

 carded and the variable would read : 



(4) vooVh, or V : v :: VH : ^h. 



Verify the truth of this mathematically derived law. 



(V) Discharge. The discharge of liquid flowing 

 through an orifice must equal the product of the 

 area of the orifice and the velocity with which the 

 liquid flows. Let D equal the quantity of liquid 

 discharged from the nozzle in a unit of time, and r 

 equal the radius of the lumen of the discharging 

 tube or orifice. Derive the formulae: 



(5) D = 4 4.37rrVh. 



(6) D xrVh. 



Where one has to deal with two variables he may 

 make one of them constant and verify for the other. 

 When r is constant: 



(7) D xVh, or D : d :: VH : ^h. 

 When the height is constant: 



(8) D xr 3 , or D : d :: R 2 : r 2 



Verify by experiment formula (7) as follows: 



During a unit of time allow the water to flow from the 



6 mm. nozzle, meantime maintaining a fixed level 



e. g., at 64 cm. by pouring water into the reservoir 



from a flask. Note the amount of discharge (D). 



Make the observation also for the 36 cm. height. 



Verify formula (8) by determining D when the 



height is kept constant (64 cm.) and the radius of 



the discharge tube alone is varied. Use, for example. 



a 3 mm. nozzle. But there is another variable not 



considered above, namely, the resistance. 



(^/) The relation of discharge to resistance. Attach to 



the nozzle one length of 6 mm. tubing. Note the 



