Horsepower and Hydraulics

Discharge of water through pumping is a result of conversion of electric horsepower via mechanical horsepower to water horsepower. Entire mechanism acts in a manner that electric motor takes electrical energy and convert it into mechanical energy, then the pump turns mechanical energy into hydraulics energy. 

The electrical energy is measured in motor horsepower (MHp), similarly mechanical energy is measured in brake horsepower (BHp) and the hydraulics energy is taken as water horsepower (WHp).

Horsepower is the amount of energy for lifting a particular weight in air to a specified distance in a particular time period. One horsepower is the amount of energy to produce 33000 lbs-ft of work per minute (33000 lbs-ft / minute). That means one horsepower lifts the weight of 33000 lbs to one feet distance in a minute, or lift 1 pound weight to 33000 feet distance in a minute.

When a pump is installed to lift and discharge water, its performance is measured in flow (gallons per minute) and pressure (feet of head). That means pump lift gallon of water and discharge at certain distance in feet in certain time period denoted in minutes.

If we multiply them with each other the resultant will be gallon - feet per minute. As we know gallon of water weighs 8.34 pounds, thus if we convert the gallon in pound (8.34 x gallons = pounds of water) , the resultant unit will be lbs - ft (of water) per minute analogous to unit of horsepower. Let's convert it into water horsepower by dividing by 33000 lbs - ft / minute per Hp.

.

WHP=  (8.34 x GPM x Feet)/HP

WHP=  (8.34 x GPM x Feet)/(33000 lb-ft ⁄ minute)

WHP=  (GPM x Feet)/3960

When the desired water horsepower are known, brake horsepower for required pump are calculated.

Brake horsepower is an amount of energy required to go into pump to produce required WHp. Taking account of friction and heat that develops in pumps during running, it is understood that pump efficiency must be affected and energy 'IN' would be needed more than energy 'OUT'. It means if pump is 80% efficient, it requires 25 BHp to generate 20 WHp as given below.

decimal equivalent of 80% is 0.80

BHp = WHp / Pump Efficiency

BHp = WHp / 0.80

if WHp is known to be 20

BHp = 20 /0.80

BHp = 25

When desired BHp are known, motor horsepower for motor can be calculated.

Similarly motor horsepower is the amount of energy that must go into motor to produce required BHp. Friction and heat in motor while running loses its efficiency thus energy required to go into motor must be more than the energy goes out to produce BHp. If motor is 90% efficient, it requires 27.77 MHp to generate 25 BHp as given below.

decimal equivalent of 90% is 0.90

MHp = BHp / Motor Efficiency    

 or        

MHp = WHp / (Motor Eff. x Pump Eff.)

If BHp is known to be 25

MHp = 25 / 0.90

MHp = 27.77

Thus the pump of 25 BHp and the motor of 27.77 say 28 MHp delivers 20 WHp of water.

Motor Horsepower can be converted into Kilowatts by multiplying MHp by 0.746 as 0.746 Kilowatts is equal to HP.

Similarly Kilowatt-hours are calculated by multiplying Kilowatts by run time in hour.

To understand entire phenomenon of calculations practically, go through this example and you will easily understand the entire mechanism and calculation.

Example: Pump data is given as 

Negative Suction Head = 6 Feet

Discharge Head  = 110 feet

Friction Loss = 19 feet

Flow = 700 GPM

Motor Efficiency = 95%

Pump Efficiency  = 85%

Solution:

Static Head = Negative Suction Head + Discharge Head

                                                           = 6 + 110 

                                                           = 116 ft

Total Dynamic Head = Negative Suction Head + Discharge Head + Friction Loss

                                                     = 6 + 110 + 19

                                                      = 135 ft

Water Horsepower that pump delivers 

WHp = (GPM x Feet) / 3960

WHp = (700 x 135) / 3960

Water Horsepower = 23.86 say 24 WHp

Brake Horsepower = WHp / Pump Efficiency

Pump Efficiency = 85% = 0.85

Brake Horsepower = 24 / 0.85

Brake Horsepower = 28.23 say 28 BHp

Motor Horsepower = BHp / Motor Efficiency

Motor Efficiency = 95% = 0.95

Motor Horsepower = 28 / 0.95

Motor Horsepower = 29.47 say 30 MHp

Kilowatts of electricity that motor of 30 MHp requires

MHp x 0.746 Kw/Hp 

30 x 0.746 = 22.38 say 22 Kw

If the pump runs 16 hours a day and the rates of electricity are $0.08 / Kw - hour. How much does it cost to run a pump for a month?

Kw - hour per day = 22 x 16 = 352

Cost per day = 352 x 0.08 = $28.16 / day

Cost for month = 28.16 x 30 = $844.8 / month

To my understanding it is known to all water operators (who work in water supply and waste water pumping plants), that how a pumping of water takes place. Even though i mean to describe it in simple manner so that it is cleared to all who feel some difficulty in understanding it. 

I hope whole concept of  conversion of energy from motor horsepower to water horsepower (hydraulics) is simplified in this piece of writing.

Also see Water treatment dosage calculations