Answers for More Math Problems &

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)(d²)(depth, ft)(7.48 gal/ft³) = (0.785)(50²)(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

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?

1 psi

2.31 ft

40 ft

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?

1 psi

80 psi

2.31 ft

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 6-ft wide channel if the flow is 18 inches deep and the velocity is 2 fps,

Flow Rate, cfs = (Cross-sectional Area, sf) (Velocity, ft/sec)

Cross-sectional Area, sf = (Length, ft) (Depth, ft)

Depth, ft = Depth, in ÷ 12 in/ft = 18 in ÷ 12 in/ft = 1.5 sf

Cross-sectional Area, sf = (Length, ft) (Depth, ft) = (6 ft)(1.5 ft) = 9 sf

Flow Rate, cfs = (Cross-sectional 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^oC. What is this in ^oF?

^oF = (^oC)(1.8) + 32 = (16^oC)(1.8) + 32 = 28.8 + 32 = 60.8^oF

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?

(C₁)(V₁) = (C₂)(V₂)

(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?

(C₁)(V₁) = (C₂)(V₂)

(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.

With no influent flow, one pump will empty the wet well in _______ minutes

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

With no influent flow and one pump running, the water level in the wet well will drop ________ feet in 10 minutes

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

Your sludge pump has one 12-inch piston with a 9-inch 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^oF and the digester is at 95^oF, how many BTUs are required to warm the sludge?

Your sludge pump has one 12-inch piston with a 9-inch 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?

Your sludge pump has one 12-inch piston with a 9-inch 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?

Your sludge pump has one 12-inch piston with a 9-inch 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?

Your sludge pump has one 12-inch piston with a 9-inch 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?

If a pump has one 12-inch piston with a 9-inch stroke, and is rated at 50 RPM, how many gpm will this pump deliver?

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.