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=LxW
= 18 x 4
= 72 m2
2. Calculate the surface area of a circular sand filter that has a diameter of 15 m.
A = π R2
= 3.14 x 7.52
= 176.71 m 2
= 177 m2
or
A = π D2
4
= 3.14 x 152
4
= 176.71 m2
= 177 m2
3. Calculate the volume of a raw water intake crib that is 8 m long, 3 m wide and 6 m
deep.
V = LxWxD
=8x3x6
= 144 m3
4. What is the volume of a cylindrical storage tank that is 7 m in diameter and 15 m high?
V = π R2 x H
= 3.14 x 3.52 x 15
= 577.26m3
= 577 m3
V = π D2 x H
4
= 3.14 x 72 x 15
4
= 2309.07
4
= 577.26 m3
= 577 m3
5. What is the volume of water contained in 84 m of a 10 cm diameter pipe?
a) in m3 - .660 m3
b) in L – 660 L
V = π R2 x H
= 3.14 x .052 x 84
= .660 m3
.660 m3 x 1000 = 660 L
OR
V = π O2 x H
4
= 3.14 x .102 x 84
4
= 2.639
4
= .660 m3 x 1000 =
660 L
6. if a pump delivers 1.44 m3in 20 min, what is the pumping rate
expressed in:
a) L/s? - 1.2 L/s
b) m3/d? – 103.68 m3/d
a) 1.44 x 1000 = 1440 L divide 20 = 72 L/min
72 L = 1.2 L/s
60 sec.
b) 1.44 = .072 m3/min.
20
.072m3/min x 1440 = 103.68 m3
**NOTE PROBLEM 6 HAS SEVERAL SOLUTIONS**
7. How many m3 of water will a 5L/s pump deliver in 5 min?
1000 L = 1 m3
5 L = .005 m3/s
.005 m3 x 60 sec. x 5 min.
1.5 m3/5 min
8. A 12 m3 storage tank supplies alum for coagulation at a rate of 330 mL/min. How
often will the tank need refilling?
12 m3 x 1000 L = 12,000 L
m3
12,000 L = 3636.36 m
.330 mL/min
9. The prechlorination chamber at a water treatment plant has a volume of 225 m3. if
the flow rate out of the tank is 11 L/s, what is the average detention time in hours.
225 m3 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
10. How many kg of chlorine are required each day to treat 18,000 m3 with chlorine
at 5.0 mg/L?
5.0 mg/L = 5 kg/1000 m3
18000 m3 x 5 kg
1000 m3
1
90 kg
5mg
L
18000 m3
day
1000L
m3
1kg
10000000 mg
11. A gas chlorinator treats 2,700 m3 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
27 L
.74 mg/L – 0.27 mg/L = .74 mg/L
1m1.L = 1 kg/m3
.74 mg/L = .74 kg/m3
2 kg
=
3
2700 m
1 kg
X
2 kg x = 2700 kg/m3
X = 2700 m3 kg
2 kg
X = 1350 m3
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
13. A mixture of water and powdered carbon is to be 85% water. if the total volume
of solution required is 3.6 m3, what is the mass of the powdered carbon?
3.6 m3 = 100%
3.6 m3 x 85% = 3.06 m3 water
3.6 m3 – 3.06 m3 = .54 m3
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
100 X
300 divide 12 = 25 kg required
b) 1 kg = 1 L – 25 kg = 25 L