OIT PRACTICE MATH QUIZ 6 DETAILED CALCULATIONS ANSWERS
1. Calculate the surface area of a rectangular tank 18 m long and 4 m wide.
A = L x W
= 18 x 4
= 72 m^{2}
2. Calculate the surface area of a circular sand filter that has a diameter of 15 m.
A = π R^{2 }^{ } or A = π D^{2}
^{ }= 3.14 x 7.5^{2 4}
^{ } = 176.71 m ^{2 } = 3.14 x 15^{2}
= 177 m^{2 }4
= 176.71 m^{2}
= 177 m^{2}
3. Calculate the volume of a raw water intake crib that is 8 m long, 3 m wide and 6 m
deep.
V = LxWxD
= 8 x 3 x 6
= 144 m^{3}
4. What is the volume of a cylindrical storage tank that is 7 m in diameter and 15 m high?
V = π R^{2} x H V = π D^{2} x H
= 3.14 x 3.52 x 15 4
= 577.26m^{3} = 3.14 x 72 x 15
= 577 m^{3} 4
= 2309.07
4
= 577.26 m^{3}
= 577 m^{3}
5. What is the volume of water contained in 84 m of a 10 cm diameter pipe?
a) in m3  .660 m^{3} V = π R^{2} x H V = π O2 x H
= 3.14 x .052 x 84 OR 4
b) in L – 660 L = .660 m^{3} = 3.14 x .102 x 84
.660 m^{3} x 1000 = 660 L 4
= 2.639
4
= .660 m^{3} x 1000 =
660 L

if a pump delivers 1.44 m3in 20 min, what is the pumping rate
expressed in:
a) L/s?  1.2 L/s a) 1.44 x 1000 = 1440 L divide 20 = 72 L/min
72 L = 1.2 L/s
b) m3/d? – 103.68 m^{3}/d 60 sec.
b) 1.44 = .072 m^{3}/min.
20
.072m^{3}/min x 1440 = 103.68 m^{3}
**NOTE PROBLEM 6 HAS SEVERAL SOLUTIONS**

How many m^{3 }of water will a 5L/s pump deliver in 5 min?
1000 L = 1 m^{3}
5 L = .005 m^{3}/s
.005 m^{3} x 60 sec. x 5 min.
1.5 m^{3}/5 min

A 12 m^{3} storage tank supplies alum for coagulation at a rate of 330 mL/min. How often will the tank need refilling?
12 m^{3} x 1000 L = 12,000 L
m^{3}
12,000 L = 3636.36 m
.330 mL/min

The prechlorination chamber at a water treatment plant has a volume of 225 m^{3}. if the flow rate out of the tank is 11 L/s, what is the average detention time in hours.
225 m^{3} x 1000 = 225000 L
225000 L = 20454.545 s
11 L/s 340.91 min
5.68 hrs or 5.7 hrs
5 hr. 60 min. x .7 = 42 min = 5 hr 42 min

How many kg of chlorine are required each day to treat 18,000 m^{3} with chlorine at 5.0 mg/L?
5.0 mg/L = 5 kg/1000 m^{3}
18000 m^{3} x 5 kg
1000 m^{3} 1
90 kg
5mg 18000 m^{3} 1000L 1kg
L day m^{3} 10000000 mg
11. A gas chlorinator treats 2,700 m^{3} with 2 kg of chlorine each day. Calculate the dosage rate. the residual is measured at 0.27 mg/L. What is the chlorine demand?
a) in mg/L  .74 mg/L 2700 x 1000 = 2700000 L
2 kg x 10000000 = 20,000000 mg
b) in kg/d
20 mg = .74 mg/L 2 kg = 1 kg
27 L 2700 m^{3} X
.74 mg/L – 0.27 mg/L = .74 mg/L 2 kg x = 2700 kg/m^{3}
X = 2700 m^{3} kg
1m1.L = 1 kg/m^{3} 2 kg
.74 mg/L = .74 kg/m^{3} X = 1350 m^{3}
12. A liquid solution with a total mass of 97 kg contains 84 kg of water and the remainder is alum
a) Calculate the percent that is water. – divide water by total multiply by 100
b) Calculate the percent that is alum. – 100 %  % of water = % of alum.
a) 84 x 100 = 8400 = 86.6 % water
97 1 97 100 %  86.6 % = 13.4 % alum

A mixture of water and powdered carbon is to be 85% water. if the total volume of solution required is 3.6 m^{3}, what is the mass of the powdered carbon?
3.6 m^{3} = 100%
3.6 m^{3} x 85% = 3.06 m^{3} water
3.6 m^{3} – 3.06 m^{3} = .54 m^{3}
or
100%  85% = 15%
3.6 m3 x .15 = .54 m3
14. A hypochlorite solution contains 12% available chlorine. if 3 kg of availible chlorine
are needed to disinfect a main:
a) how many kg of solution are required?
b) How many litres of solution are required
3 kg = 12%
a) 12% = 3 300 divide 12 = 25 kg required

X
b) 1 kg = 1 L – 25 kg = 25 L 