 
Answers for More
Math Problems & Charts
Click here to return to
More Math Problems and Charts
The controls for a
pump are set for the pump to turn on when the pressure drops to 2
psi and to turn off when the pressure reaches 8 psi. If this
tank has a diameter of 50 feet, how many gallons will be stored
between pumping cycles?
Diameter = 50 feet and from the solution below,
depth = 13.86 ft
Volume, gallons =
(0.785)(d^{2})(depth, ft)(7.48 gal/ft^{3}) =
(0.785)(50^{2})(13.86)(7.48) =
203,458 gallons
The controls for a
pump are set for the pump to turn on when the pressure drops to 2
psi and to turn off when the pressure reaches 8 psi. Calculate
the following items:
1. The depth of liquid when the pump turns
on
(2 psi)(2.31
ft/psi) = 4.62 ft
2. The depth of the liquid when the pump
turns off
(8 psi)(2.31
ft/psi) = 18.48 ft
3. The depth of the liquid that can be
pumped
18.48 ft  4.62
ft = 13.86 ft
A centrifugal pump delivering
200 gpm against a total head of 40
feet produces _______ HP
WHP = (Flow, gpm)(Head, ft) ÷ 3,960
= (200 gpm)(40 ft) ÷ 3,960 = 2 WHP
A lot which
measures 1200 feet by 1500 feet contains ______ acres
(1200 feet)(1500 ft) = 1,800,000 square feet
(1,800,000 square feet)
÷ (43,560 sf/acre) =
41.3 acres
3
cubic yards contains _____ cubic feet
(3 cubic yards)(27 cubic feet/cubic yard) =
81 cubic feet
1 yard = 3 feet
1 cubic yard = (1 yard)(1 yard)(1
yard) = (3 ft)(3 ft)(3 ft) = 27 cubic feet
Calculate the pumping rate for a pump if the wet well drops
4 feet in 30
minutes. The wet well is 12 feet wide and
15 feet long.
Volume, cf = (Length,
ft)(Width, ft)(Depth, ft) = (15 ft)(12 ft)(4 ft) = 720 cf
Capacity, gal =
(Volume, cf)(7.48 gal/cf) = 5,385.6 gal
Flow, gpm =
(Capacity, gal) ÷ (Time, min) = 5,385.6 gal ÷ 30 minutes =
180 gpm
If you dig a trench 500 feet long, 3 feet wide, and 8 feet deep, how
many cubic yards of spoil will you remove?
Volume, cf = (Length,
ft)(Width, ft)(Depth, ft) = (500 ft)(3 ft)(8 ft) = 12,000 cf
Volume, cy = (Volume,
cf) ÷ (27 cf/cy) = 444 cy
What is the discharge pressure of your pump if you're
pumping into a force main that is 40 feet above the pump and you
need to maintain a pressure of 60 psi in the force main?
Have
you tried using my box converter to solve this type of problem?
To learn more about how to use the box
converter, click here
Steve's Box
Converter
or YouTube
and see video (http://www.youtube.com/watch?v=zgRSE23h3sY&feature=channel).
40 ft
÷ 2.31 ft/psi =
17.3 psi
Discharge pressure = 60 psi + 17.3 psi = 77.3 psi
If the
discharge pressure gauge reads 80 psi, what is the equivalent head in feet?
Have
you tried using my box converter to solve this type of problem?
To learn more about how to use the box
converter, click here
Steve's Box
Converter
or YouTube
and see video (http://www.youtube.com/watch?v=zgRSE23h3sY&feature=channel).
2.31 ft/psi x 80 psi =
184.8 ft
Calculate the
flow in cfs for a 6ft wide
channel if the flow is 18 inches deep and the velocity
is 2 fps,
Flow Rate, cfs = (Crosssectional
Area, sf) (Velocity, ft/sec)
Crosssectional
Area,
sf = (Length, ft) (Depth,
ft)
Depth, ft = Depth, in ÷ 12 in/ft = 18 in
÷ 12 in/ft = 1.5 sf
Crosssectional
Area,
sf = (Length, ft) (Depth,
ft) = (6 ft)(1.5 ft) = 9 sf
Flow
Rate, cfs = (Crosssectional Area, sf)
(Velocity, ft/sec) = (9 sf)(2 fps) =
18 cfs
6 mgd = _________ cfs
6 mgd x 1.55 cfs/mgd =
9.3 cfs
The temperature of your sample is
16^{o}C. What is this in ^{o}F?
^{o}F
= (^{o}C)(1.8) + 32 = (16^{o}C)(1.8) + 32 = 28.8 + 32 =
60.8^{o}F
If you thicken your solids from
2% to 5% and you typically pump 1000 gallons per day of 2%, how many gallons
of 5% solids will you pump?
(C_{1})(V_{1})
= (C_{2})(V_{2})
(5%)(??? gallons) = (2%)(1000 gallons)
(5%)(???
gallons) = 2000%gallons
(??? gallons) ÷ 5% =
(2000%gallons) ÷ 5% =
400 gallons
If you thicken your solids from
4% to 6% and you typically pump 12,000 gallons per day of 4%, how many gallons
of 6% solids will you pump?
(C_{1})(V_{1})
= (C_{2})(V_{2})
(6%)(??? gallons) = (4%)(12,000 gallons)
(6%)(???
gallons) = 48,000%gallons
(6%)(???
gallons) ÷ 6% = (48,000%gallons) ÷ 6% =
8,000 gallons
A lift
station is equipped with three pumps, each rated at 175 gpm. The wet well is
20 feet long, 10 feet wide, and 9 feet deep. The average
influent
flow is
0.5 mgd.
20 ft x 10 ft x 9 ft = 1,800 cf
1,800 cf x 7.5 gal/cf = 13,500 gal
13,500 gal ÷ 175 gpm =
77.1 min
10 min ÷ 77.1 min = 0.13
0.13 x 9 ft = 1.17 ft
Given
this lab
data,
calculate the TSS in mg/L

Tare Weight = 20.0012
g

Final Dry Weight = 20.0015
g

Sample Volume = 50 mL
Solids, mg/L =
(Dry Solids, grams)(1,000,000)
Sample Volume, mL
Dry Solids, g =
Final Dry Weight, g  Tare Weight, g
= 20.0015 g  20.0012 g = 0.0003 g
Solids, mg/L =
(0.00030 g)(1,000,000)
50 mL
= 300 ÷ 50
= 6 mg/L
Your sludge
pump has one
12inch piston with a 9inch
stroke. It is rated at 50 RPM
and
is set to pump 2
minutes every 10
minutes. The total solids concentration
is 5%. If the temperature of the raw sludge is 50^{o}F and the
digester is at 95^{o}F, how many BTUs are
required to warm the sludge?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm

Calculate gpd of sludge
(220 gpm)(2 min/10 min)(1440 min/day) =
63,360 gpd of sludge

Convert to lbs/day of sludge
(63,360 gpd)(8.34 lbs/gal) = 528,422 lbs/day of sludge

Calculate the temperature increase
95^{o}F  50^{o}F = 45^{o}F

Calculate the BTUs required
(528,422 lbs/day of sludge)(45^{o}F)
= 23,778,990 BTUs
Your sludge pump has one
12inch piston with a 9inch
stroke. It is rated at 50 RPM
and
is set to pump 2
minutes every 10
minutes. The total solids concentration
of the sludge is 5% and the volatile solids concentration is 70%.
Your digester typically produce 12 cubic feet of digester gas per
pound of volatile solids fed to the digester and averages 650
BTU/cubic foot of digester gas, how many
BTUs should be produced?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm

Calculate gpd of sludge
(220 gpm)(2 min/10 min)(1440 min/day) =
63,360 gpd of sludge

Convert to lbs/day of sludge
(63,360 gpd)(8.34 lbs/gal) = 528,422 lbs/day of sludge

Convert %Total Solids (TS) to
decimal equivalent
5% TS ÷ 100 = 0.05 TS

Calculate lbs/day of Total Solids
(528,422 lbs/day of sludge)(0.05
TS) = 26,421 lbs/day of TS

Calculate lbs/day of Volatile Solids
(26,421 lbs/day of TS)(0.70 VS) =
18,495 lbs/day of
VS

Calculate lbs/day of cubic feet of
digester gas produced
(18,495 lbs/day of
VS)(12 cf/lb) = 221,940 cubic of digester gas
produced

Calculate the BTUs produced
(221,940 cf)(650 BTU/cf) =
14,261,000 BTU
OR

Convert to MGD of sludge
(63,360 gpd)
÷
(1,000,000 gpd/MGD) = 0.06336 MGD

Convert %Total Solids (TS) to
mg/L
(5% TS)(10,000 mg/L/%)= 50,000
mg/L TS

Calculate lbs/day of Total Solids
(50,000 mg/L)(8.34 lbs/gal)(0.06336 MGD) = 26,421 lbs/day of TS

Calculate lbs/day of Volatile Solids
(26,421 lbs/day of TS)(0.70 VS) =
18,495 lbs/day of
VS

Calculate lbs/day of cubic feet of
digester gas produced
(18,495 lbs/day of
VS)(12 cf/lb) = 221,940 cubic of digester gas
produced

Calculate the BTUs produced
(221,940 cf)(650 BTU/cf) =
14,261,000 BTU
Your sludge
pump has one
12inch piston with a 9inch
stroke. It is rated at 50 RPM
and
is set to pump 2
minutes every 10
minutes. The total solids concentration
of the sludge is 5% and the volatile solids concentration is 70%.
If your digester typically produce 12 cubic feet of digester gas per pound of
volatile solids fed to the digester, how many cubic
feet of digester gas should be produced?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm

Calculate gpd of sludge
(220 gpm)(2 min/10 min)(1440 min/day) =
63,360 gpd of sludge

Convert to lbs/day of sludge
(63,360 gpd)(8.34 lbs/gal) = 528,422 lbs/day of sludge

Convert %Total Solids (TS) to
decimal equivalent
5% TS ÷ 100 = 0.05 TS

Calculate lbs/day of Total Solids
(528,422 lbs/day of sludge)(0.05
TS) = 26,421 lbs/day of TS

Calculate lbs/day of Volatile Solids
(26,421 lbs/day of TS)(0.70 VS) =
18,495 lbs/day of
VS

Calculate lbs/day of cubic feet of
digester gas produced
(18,495 lbs/day of
VS)(12 cf/lb) = 221,940 cubic of digester gas
produced
OR

Convert to MGD of sludge
(63,360 gpd)
÷
(1,000,000 gpd/MGD) = 0.06336 MGD

Convert %Total Solids (TS) to
mg/L
(5% TS)(10,000 mg/L/%)= 50,000
mg/L TS

Calculate lbs/day of Total Solids
(50,000 mg/L)(8.34 lbs/gal)(0.06336 MGD) = 26,421 lbs/day of TS

Calculate lbs/day of Volatile Solids
(26,421 lbs/day of TS)(0.70 VS) =
18,495 lbs/day of
VS

Calculate lbs/day of cubic feet of
digester gas produced
(18,495 lbs/day of
VS)(12 cf/lb) = 221,940 cubic of digester gas
produced
Your sludge
pump has one
12inch piston with a 9inch
stroke. It is rated at 50 RPM
and
is set to pump 2
minutes every 10
minutes. The total solids concentration
of the sludge is 5% and the volatile solids concentration is 70%, how many pounds of
volatile solids
are pumped daily?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm

Calculate gpd of sludge
(220 gpm)(2 min/10 min)(1440 min/day) =
63,360 gpd of sludge

Convert to lbs/day of sludge
(63,360 gpd)(8.34 lbs/gal) = 528,422 lbs/day of sludge

Convert %Total Solids (TS) to
decimal equivalent
5% TS ÷ 100 = 0.05 TS

Calculate lbs/day of Total Solids
(528,422 lbs/day of sludge)(0.05
TS) = 26,421 lbs/day of TS

Calculate lbs/day of Volatile Solids
(26,421 lbs/day of TS)(0.70 VS) =
18,495 lbs/day of
VS
OR

Convert to MGD of sludge
(63,360 gpd)
÷
(1,000,000 gpd/MGD) = 0.06336 MGD

Convert %Total Solids (TS) to
mg/L
(5% TS)(10,000 mg/L/%)= 50,000
mg/L TS

Calculate lbs/day of Total Solids
(50,000 mg/L)(8.34 lbs/gal)(0.06336 MGD) = 26,421 lbs/day of TS

Calculate lbs/day of Volatile Solids
(26,421 lbs/day of TS)(0.70 VS) =
18,495 lbs/day of
VS
Your sludge
pump has one
12inch piston with a 9inch
stroke. It is rated at 50 RPM
and
is set to pump 2
minutes every 10
minutes. If the total solids concentration
is 5%, how many pounds of
total solids
are pumped daily?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm

Calculate gpd of sludge
(220 gpm)(2 min/10 min)(1440 min/day) =
63,360 gpd of sludge

Convert to lbs/day of sludge
(63,360 gpd)(8.34 lbs/gal) = 528,422 lbs/day of sludge

Convert %Total Solids (TS) to
decimal equivalent
5% TS ÷ 100 = 0.05 TS

Calculate lbs/day of Total Solids
(528,422 lbs/day of sludge)(0.05
TS) = 26,421 lbs/day of TS
OR

Convert to MGD of sludge
(63,360 gpd)
÷
(1,000,000 gpd/MGD) = 0.06336 MGD

Convert %Total Solids (TS) to
mg/L
(5% TS)(10,000 mg/L/%)= 50,000
mg/L TS

Calculate lbs/day of Total Solids
(50,000 mg/L)(8.34 lbs/gal)(0.06336 MGD) =
26,421 lbs/day of TS
Your sludge
pump has one
12inch piston with a 9inch
stroke. It is rated at 50 RPM
and
is set to pump 2
minutes every 10
minutes. How many gallons of sludge are pumped daily?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm

Calculate gpd
(220 gpm)(2 min/10 min)(1440 min/day) =
63,360 gpd
If a pump has one 12inch
piston with a 9inch stroke, and is rated at
50 RPM, how many gpm will this pump deliver?

Convert inches to feet
12 inch piston ÷ 12 in/ft = 1 ft
9inch stroke ÷ 12 in/ft = 0.75
ft

Calculate the volume displaced for
one stroke
(0.785)(1 ft)(1 ft)(0.75
ft)(7.48 gal/ft) = 4.4 gal/stroke

Calculate the gpm (RPM =
strokes/min)
4.4 gal/stroke x 50 RPM =
220 gpm
To determine the weight of a tank, you should:
A. Calculate the volume
in gallons and divide by 1,000,000
B. Calculate the volume
in gallons and multiply by 8.34
C. Divide the depth by 2.31
D. Divide the volume by the flow
The correct answer is
B. Calculate the volume and multiply by 8.34
A is incorrect. This
is how you would calculate the volume in million gallons
C is incorrect. This
is how you would calculate the pressure on the bottom of the tank
D is incorrect. This
is how you would calculate detention time.
mg/L x 8.34
x MGD is the formula for calculating
A.
Chlorine demand
B. lbs
C. lbs/day
D.
Volume of a cylindrical tank
The correct answer is
C. lbs/day
Click on the
thumbnail below for the answers for the chart of pump station math
for cylindrical tanks.
Click on the
thumbnail below for the answers for the chart of pump station math
for rectangular tanks.
Click on the
thumbnail below for the answers for the chart of pipe math.
Match 
1 
The units for pressure are 
A 
Divided by 
2 
Head is expressed in 
B 
2.31 
3 
Velocity is measured in 
C 
0.434 psi 
4 
Units of flow 
D 
psi 
5 
Pressure times _______ = Head 
E 
fps 
6 
Head __________ 2.31 = Pressure 
F 
1440 
7 
20 psi = 
G 
694 gpm 
8 
1 MGD = 
H 
cfs 
9 
A head loss of 7 feet = 
I 
3 psi 


J 
Times 


K 
ft 


L 
46.2 ft 


M 
Subtracted by 
1 = D
2 = K
3 = E
4= H
5 = B
6 = A
7 = L
8 = G
9 = I
The formula for the volume of
a rectangular tank is
A. (Length)(Width)
B.
(0.785)(Diameter^{2})
C. (Length)(Width)(Height)
D.
(0.785)(Diameter^{2})(Height)
The correct answer is C. (Length)(Width)(Height)
A is the formula for the area of
a rectangle
B is the formula for the area of
a circle
D
is the formula for the volume of a cylinder
The formula for the volume of
a cylindrical tank is
A. (Length)(Width)
B.
(0.785)(Diameter^{2})
C. (Length)(Width)(Height)
D.
(0.785)(Diameter^{2})(Height)
The correct answer is D.
(0.785)(Diameter^{2})(Height)
A is the formula for the area of
a rectangle
B is the formula for the area of
a circle
C is the formula for the volume
of a rectangle
Given a tank measures 50
feet long, 25 feet wide, and 15 ft deep, calculate:
 Surface area in ft^{2}
 Crosssectional area in
square feet
 Volume in cf
 Capacity in gallons
The correct answers are:
Surface area in ft^{2}
= Length, ft x Width, ft = 50 ft x 25 ft = 1250 ft^{2}

Crosssectional area in square feet
Crosssectional area in ft^{2} = Width, ft x Depth, ft = 25 ft x
15 ft =
375 square feet
Volume in cf = Length, ft x Width, ft x
Depth, ft = 50 ft x 25 ft x 15 ft =
18,750 cf
Capacity in gallons = Vol in cf x 7.5
gal/cf = 18,750 cf x 7.5 gal/cf =
140,625 gal
For questions or comments,
call 5153131159
Click here to return to
More Math Problems and Charts
Home
