In this blog we discuss the mathematics involved in water hydraulics to calculate flows, pressures, volumes and velocities etc. Its knowledge is a key for the water operators and workers of municipal sector involved particularly in water supply and waste water management operations.

This blog covers most of the major categories of maths calculations that are important to know for daily operations of water system. Let's deal with them one by one.

## PRESSURE

Water pressure is measured in terms of pounds per square inch (psi) and feet of head (height of water column in feet).

A 2.31 feet high water column creates a pressure of 1 psi. In this way the water pressure at the bottom of a storage tank can be used for determining the water level in the tank by using this relation of pressure units i.e head and psi.

Centrifugal pumps used to pump the water are rated in feet of Total Dynamic Head (TDH) but the system pressures are measured in psi.

Thus it is necessary for water operators to become familiar with conversion of pressure units from one to other.

If the pressure (psi) is known, the height of the water column (Head) can be determined by multiplying the known value in psi by 2.31.

psi x 2.31 = Feet of Head ----------- (a)

Example:

- A pressure gauge at the bottom of water storage tank reads pressure as 30 psi. What is the water level in the tank? or what is the head of water column in feet?

- The level of reservoir is 115 feet above the pump discharge. What is the discharge pressure on the pump?

- If a pump is installed at 5320 feet above sea level. The overflow of the reservoir is stationed at 5460 feet above sea level. What will be the discharge pressure on the pump in psi?

- If a discharge pressure gauge on a pump reads 72 psi when the pump is running. The pressure gauge at the top of a hill on 40 feet height above the pump reads 45 psi. What is the friction loss in pipe in feet of head?

## FLOW

- A system uses 2 mgd. How many gallons per minute does it use?

- If a pipeline has a carrying capacity of 3 cfs. How many gpm can it handle?

- A well pumps 350 gpm. How many mgd will it pump?

### Water meters

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## DAE MJP-75 Lead Free Potable Plastic Water Meter, 3/4" NPT Couplings, Gallon |

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## AREAS

- Area = d
^{2 }x 0.785 where 'd' is diameter of circle - Area = r
^{2 }x 3.1416 where 'r' is radius of circle

- A sedimentation basin is 60 feet in diameter. What is the surface area of the tank?

- A pipeline has diameter of 12 inches. What is the area of the pipe?

## VOLUMES

^{}

- If a sedimentation basin is 60 feet long & 40 feet wide and 10' deep. What will be the volume of the tank in cubic feet?

^{2 }x 3.1416 x H

^{2 }x 0.785 x H

- If a sedimentation basin is 60' in diameter and 12' deep. What is the volume of the tank?

## VOLUME IN GALLONS

- Sedimentation basin is 60 feet long and 40 feet wide and 10' deep. What is the volume of tank in cubic feet?

- If a circular tank has a diameter of 40 feet and is 10 feet deep. How many gallons will it hold?

## VOLUME OF PIPES

- A 12" line is 1100 feet long. How many gallons does the pipe hold?

- A 6" line is 654 feet long. How many gallons does the pipe hold?

## VELOCITY

- If a 24" pipe carries a flow of 11 cfs. What is the velocity in the pipe?

- A 12" pipe carries water at the velocity of 5 feet per second (fps). What is the flow in cfs?

- A 12" pipe carries 1400 gpm at 4 fps velocity and reduces to a 6" pipe. What is the velocity in the 6" pipe?

## DETENTION TIME

- A 50,000 gallons tank receives 250,000 gpd flow. What is the detention time in hours?

- A tank is 60' x 80' x 10' and the flow is 2 mgd. What is the detention time in hours?

- If a tank is 100 feet in diameter and 22 feet deep. If flow into the tank is 1500 gpm and the flow out of the tank is 300 gpm. What time in hours will it take to fill the tank?

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