348 CALCULATIONS for 



N°. XLI. 



Calculations relating to Grijl and Saw Mills, for determin- 

 ing the quantity of JVatcr necejfary to produce the de/ircd 

 cjj'ccl when the Head and Fall are given in order to a/cer- 

 tain the dimenfions of a new invented Steam Engine, in- 

 tended to give Jiiotion to Water-wheels in places where 

 ,,jere is no Fall^ and but a very/mall Stream or Spring. 

 By John N a n c a r row. 



ELEMENTS ufed in the following calculations, 

 fo far ?,s they relate to works moved by water- 

 wheels : 



1. let h =: mean height of the head of water in the penftock. 



2. a ■=: the area of the aperture or gateway. 



3. q ^=z6.l2%^=l the number of ale gallons in a cubic foot. 



4. s z=. \6 feet,= the fpace a heavy body falls from reft in one 



fecond. 



5. 2jr: the uniform velocity acquired by falling 16 feet from 



reft. 



6. 2y/hs, or S^^h^z the uaiform velocity acquired by fall- 



ing from reft any depth zr h. 



7. Saqy/li, the number of ale gallons ifluing through any 



aperture a in one fecond, and Saqt^h :^the quantity 

 in t feconds. 



8. Sa^h'z: the number of cubic feet flowing through a in 



one fecond, and Saf^h=: the number of cubic feet 

 in t feconds. 

 g, ^=62.5 pounds avoirdupoife,n the weight of a cubic foot 

 of water, and 10.2 lbs. rrthe weight of an ale gallon.. 



10. haw=. the weight of any column of water. 



11. — — =.t :=. the time of falling from an height ■=. h. 



4 



12. D — — is the common praftical rule for finding the mean 



height of the head of water when the aperture is 

 vertical and re(5tangular where D reprefents the depth 



of 



