Introduction - Mathematics and Statistics for the Environment - page 21

■ EXAMPLE 1.21
Problem: A liquid chemical weighs 62 lb/ft 3 . How much does a 5-gal can of it weigh?

Solution: Solve for specific gravity, determine lb/gal, and multiply by 5:

Weight of chemical (lb/ft 3

3

)
Weight of water(lb/ft)

62 lb/ft
62.4 lb

Specificgravity = = = 099 .

3 3

/ft

Weight of chemical (lb/gal)
8

0.99 =

.34 lb/gal

Weight of chemical = 8.26 lb/gal

8. 26 lb/gal × 5 gal = 41.3 lb

■ EXAMPLE 1.22
Problem: A wooden piling with a diameter of 16 in. and a length of 16 ft weighs 50 lb/ft 3 . If it is
inserted vertically into a body of water, what vertical force is required to hold it below the water
surface?

Solution : If this piling had the same weight as water, it would rest just barely submerged. Find the
difference between its weight and that of the same volume of water—that is the weight needed to
keep it down:

62.4 lb/ft 3 (water)

- 50.0 lb/ft 3 (piling)

12.4 lb/ft 3 difference

Volume of piling = 0.785 × (1.33) 2 × 16 ft = 22.21 ft 3

12.4 lb/ft 3 × 22.21 ft 3 = 275.4 lb

■ EXAMPLE 1.23
Problem : A liquid chemical with a specific gravity (SG) of 1.22 is pumped at a rate of 40 gpm. How
many pounds per day are being delivered by the pump?

Solution : Solve for pounds pumped per minute, then change to pounds/day.

8.34 lb/gal water × 1.22 SG liquid chemical = 10.2 lb/gal liquid

40 gal/min × 10.2 lb/gal = 408 lb/min

408 lb/min × 1440 min/day = 587,520 lb/day

■ EXAMPLE 1.24
Problem : A cinder block weighs 70 lb in air. When immersed in water, it weighs 40 lb. What are the
volume and specific gravity of the cinder block?

Solution: The cinder block displaces 30 lb of water; solve for cubic feet of water displaced (equiva-
lent to volume of cinder block).

30 lb waterdisplaced
62.4 lb/ft

3

= 0.48 ft w ater displaced

3