how to calculate water flow, volume and pressure

 

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?

      Formula given in (a) to convert psi to feet of head            

psi x 2.31 = feet of head     (put known values)          

30 psi x 2.31 = 69.4 feet of water above the gauge     

Hence with the reading of pressure at the bottom of storage tank we can determine the height of water columns in  feet in storage tank. Because the height of water column in feet is linked with the magnitude of pressure it can create.

In the example given above the pressure was known and we calculated the height of water column i.e Head in feet.

Similarly If the height of a column of water is known, the pressure it exerts can be determined by dividing the feet of head by 2.31.

Feet of Head / 2.31 = psi  -------------------------- (b)

Example:

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

Formula given in (b) to convert feet of head to psi 

115 / 2.31 = 49.8 psi

These were simple calculations for calculating pressure (psi) and head (feet) by putting known values of either of them in given formulas.

The advance questions may require to calculate head (feet) or pressure (psi) before it can be converted.

Example: 

• 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?

Neither we are known to head (feet) nor pressure (psi)

Now to determine the pressure (psi) we have to calculate head (feet) first

For that, find the difference in elevations given above

5460 - 5320 = 140 feet of head

Now as we know the value of head (feet), we can calculate pressure (psi)

140 /2.31 = 60.6 psi

see more examples

• 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?

Now we have got two pressure values one at pump and other is where water is being pumped

Secondly we have got 40 feet head the pump is qualifying at top of hill

And we have to determine friction loss in pipe responsible for difference in pressures

First of all we find the difference between pressures

72 psi - 45 psi = 27 psi

Now convert it into feet of head

27 x 2.31 = 62.37 feet of head

This is the total head loss

Subtract the difference in elevation to find friction loss

62.37 feet - 40 feet = 22.37 feet of head

Do it other way

Convert pressures in head

72 x 2.31 = 166.32 feet

 45 x 2.31 = 103.95 feet 

Find the difference

166.32 - 103.95 = 62.37 feet

This is the total head loss 

distance from pump to hill + friction loss in pipe = head loss -------(xx)

We have to find friction loss, re-arrange (xx)

friction loss = head loss - distance from pump to hill 

friction loss = 62.37 - 40

friction loss = 22.37 feet

FLOW

The amount of water moving through the system in unit time is called flow. It can be measured in one of the three different units. They are gpm (gallons per minute), mgd (million gallons per day) and cfs or cusec (cubic feet per second).

How they are converted from one to other

mgd = gpm / 700    ,      gpm = mgd x 700

cfs  = gpm / 449      ,     gpm = cfs x 449

Example: 

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

1 mgd = 700 gpm

thus 2 mgd x 700 = 1400 gpm

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

1 cfs = 449 gpm

thus 3 cfs x 449 = 1347 gpm

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

1 mgd = 700 gpm

1 gpm = 1 / 700 mgd

thus 350 gpm = 350 / 700 mgd = 0.5 mgd

Water meters 

DAE WP-300P 3" Woltmann Helix Water Meter, Pulse Output, Gallon

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

DAE PD-75 Lead Free Potable, Positive Displacement Water Meter, 3/4" NPT Couplings, Pulse Output, Gallon

AREAS

For the calculations of volume of circular tanks and velocities in circular pipes, the area of circle is required to be calculated.

There are two formulae used to calculate the area of circle.

1. Area = d² x 0.785      where 'd' is diameter of circle
2. Area = r² x 3.1416     where 'r' is radius of circle

For determining volume of water the Area is multiplied by the height of tank or length of pipe.

Examples: 

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

d = 60 , r = 30 

Apply both formulae

30 x 30 x 3.1416 = 2830 square feet

60 x 60 x 0.785 =   2830 square feet

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

d = 12" , r = 6"

Apply both formulae

6 x 6 x 3.1416 = 113 sq.in

12 x 12 x 0.785 = 113 sq.in

If the storage tank is rectangular instead of circular then area is determined by 

A = L x W 

where 'L' is length and 'W' is width and for calculating the volume of water in rectangular tank the third dimension i.e height (H) is multiplied.

VOLUMES

The volume of rectangular tank is calculated by multiplying length, width and height of tank.

Volume of rectangular tank (cubic feet) = L x W x H

Example: 

• 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?

We have got all three dimensions, now calculate the volume

60' x 40' x 10' = 24,000 cft

Volume of circular tank can be calculated by multiplying the area by the height (depth) of the tank.

Volume of circular tank (cubic feet) =  r² x 3.1416 x H

or 

Volume of circular tank (cubic feet) = d² x 0.785 x H

Example: 

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

d = 60'  ,  r = 30'

depth or height of tank = 12'

Applying both formulae of area to be multiplied by 'H'

30 x 30 x 3.1416 x 12 = 33,900 cubic feet

60 x 60 x 0.785 x 12 =  33,900 cubic feet

VOLUME IN GALLONS

Volume of tank or pipe is calculated in cubic feet and gallons as well. If  the volume is calculated in cubic feet (cft), it can be converted into gallons. Same conversion can be rendered from gallons to cubic feet.

Let's discuss the conversion method between cubic feet and gallons

1 cubic feet = 7.48 gallons

in other words

1 cubic feet contains 7.48 gallons

Example: 

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

L = 60' , W = 40' and H (depth or height) = 10'

Volume (cft) = 60 x 40 x 10 = 24000 cft

Now apply conversion formula from cubic feet to gallons

1 cubic feet = 7.48 gallons

24000 cubic feet = 24000 x 7.48 gallons

 24000 cubic feet = 179,500 gallons          

Means 24000 cubic feet space contains 179,500 gallons

Thus when cubic feet is known, multiply the value of cubic feet by 7.48 to get gallons

Similarly if gallons are known, they are divided by 7.48 to calculate cubic feet

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

diameter = 40 ft , radius = 20 ft

H (depth or height) = 10 feet

Calculate the volume in cubic feet

20 x 20 x 3.1416 x 10 = 12,600 cubic feet

or 

40 x 40 0.785 x 10 = 12,600 cubic feet

we calculated cubic feet volume, convert to gallons

12,600 x 7.48 =94,200 gallons

VOLUME OF PIPES

Number of gallons held in one-foot section of pipe can be determined by;

squaring diameter (in inches), then multiplying by 0.0408.

 gallons in one foot pipe section = d (inch) x d (inch) x 0.0408 

Now for determining the gallons in particular length of pipe, the same formula is further multiplied by number of feet of pipe.

Volume (gal) = d x d x 0.0408 x length (pipe)

Examples:

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

Solve it by formula given above

Volume (gallons) = 12 x 12 x 0.0408 x 1100 = 6460 gallons

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

Volume (gallons) = 6 x 6 x 0.0408 x 654 = 960 gallons

VELOCITY

The velocity of water moving through pipe can be calculated if the flow in cubic feet per second (cfs) and the diameter of pipe (inches) are known.

Area of pipe is calculated in square feet (sq.ft) and the flow is then divided by the area.

Velocity (feet per second or fps) = Flow (cfs) / Area (sq.ft)

Example:

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

change diameter from inches to feet

d = 24 / 12 = 2 feet

Now find area of pipe in sq.ft

Area (sq.ft) = 2 x 2 x 0.785 = 3.14 sq.ft

Now find velocity in feet per second

Velocity (fps) = Flow / Area = 11 / 3.14 = 3.5 fps

The flow through pipe (cfs) can be determined if the velocity and pipe diameter are known. The area of pipe is calculated in square feet and it is multiplied by velocity (fps), and the resultant is Flow (cfs).

Examples:

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

convert dia from inches to feet

d = 12 / 12 = 1 foot

Now calculate area 

Area (sq.ft) = 1 x 1 x 0.785 = 0.785 sq.ft

Now calculate flow

if Velocity = Flow / Area

Flow = Area x Velocity

Flow (cfs) =  0.785 x 5 = 3.925 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?

convert dia from inches to feet

d = 6 / 12 = 0.5 foot

find Area of pipe in sq.ft

Area (sq.ft) = 0.5 x 0.5 x 0.785

Area (sq.ft) = 0.196 sq.ft

convert flow from gpm to cfs

Flow = 1400 / 449 = 3.12 cfs

Now we have values of Flow and Area

find velocity now

Velocity (fps) = Flow (cfs) / Area (sq.ft)

Velocity = 3.12 / 0.196 = 15.92 fps 

say 16 feet per second 

DETENTION TIME

Length of time in minutes or hours for one gallon of water to pass through from tank is called 'Detention Time'.

It is calculated by using following formula

Detention time = Capacity of tank (gal) / Flow (gpm or gpd)

           = Volume (gal) / Flow (gpm or gpd)

If flow is taken in gpm, the detention time results in minutes, to change it in hours divide minutes by 60.

If flow is taken in gallons per day (gpd), the resultant detention time will be in day. To convert it into hours, multiply the result by 24 and the detention time will be converted to hours.

The formula for Detention time can also be used for calculating time to fill a tank.

Examples: 

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

Use formula of Detention time

Detention time = Volume / Flow

                          = 50000 / 250000

Detention time = 0.2 days           

Convert to hours

0.2 x 24 = 4.8 hours

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

From the dimensions of tank, it is evident that it is rectangular tank

Find volume of tank

Volume (cft) = 60 x 80 x 10 = 48000 cubic feet

Now change cubic feet to gallons

Volume (gal) = 48000 x 7.48 = 359000 gallons

Now change flow from mgd to gpd

2 mgd x 1000000 = 2000000 gpd

Now find Detention time (days)

Detention time = Volume (gal) / Flow (gpd)

    D.T (days) = 359000 / 2000000

D.T (days) = 0.18 days          

Change days to hours

0.18 x 24 = 4.3 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?

diameter = 100 feet and depth = 22 feet

Calculate volume in cubic feet

Volume (cft) = 100 x 100 x 0.785 x 22 = 173000 cubic feet

change cubic feet to gallons

Volume (gal) = 173000 x 7.48 = 1290000 gallons

Calculate net inflow

1500 gpm - 300 gpm = 1200 gpm

Calculate the time to fill (D.T)

D.T  (min) = 1290000 / 1200 

D.T (min) = 1075 minutes     

Change minutes to hours

D.T (hours) = 1075 / 60

 D.T (hours) = 17.9 hours

We will continue sharing such information for the best use of our viewers and welcome their valued comments to be incorporated in future blogs.

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