Calculations (Head and Horsepower)
1. Head to Pressure
A wastewater column 1 foot high exerts a pressure of 0.433 pounds per
square inch. The total pressure can be calculated by multiplying
the height (depth) of the water by 0.433 psi/foot. The height/depth
of the water is also called "head".
Example: The water in the settling
tank is 15 feet deep. What is the pressure in pounds per square
inch at the bottom of the tank?
2. Pressure to Head
Pressure can also be converted into its equivalent column of water or
head. A pressure of 1 psi is the same as a column of water
2.31 feet high.
Example: The pressure gauge on the discharge line of the
pump reads 45 psi. What is the equivalent head in feet?
3. Work
Work is defined as moving an object (weight) a vertical distance.
It is expressed as footpounds
Example: How much
work is performed if 200 gallons of wastewater are lifted (pumped) a vertical
distance of 50 feet?
4. Power
Power is the amount of work done per unit time. It is expressed
in foot pounds per minute.
Example: How much power in foot pounds per minute will
be needed to lift 500 gallons of wastewater a vertical distance of 75
feet in three minutes?
Head is the vertical distance the wastewater must be lifted from
the supply tank to the discharge. The total head includes
the vertical distance the liquid must be lifted (static head),
the loss to friction (friction head), and the energy required to
maintain the desired velocity (velocity head).
Example: The supply tank is
located at elevation 118 feet. The discharge point is at elevation
207 feet. What is the static head in feet?
Friction Head
Friction head is the equivalent distance of the energy which must
be supplied to overcome friction. Engineering references include
tables showing the equivalent vertical distance for various sizes
and types of pipes, fittings, and valves. The total friction
head is the sum of the equivalent vertical distances for each component.
Velocity Head Velocity head is
the equivalent distance of the energy consumed in achieving and maintaining
the desired velocity in the system.
6. Horsepower
Horsepower is a common expression for power in wastewater treatment.
One horsepower is equal to 33,000 foot pounds of work per minute.
Example: The pump lifts 649 gpm of water a vertical distance
of (head) of 105 feet. How much horsepower is used?
7. Water Horsepower
The amount of power required to move a given volume of water a specified
total head.
Example: A pump must deliver 250 gpm to total head of
95 feet. What is the required water horsepower?
8. Brake Horsepower
The amount of horsepower to be supplied to the pump to provide the required
water horsepower. The efficiency of the pump must be taken into
account.
Example: Under the specified conditions, the pump efficiency
is 76%. If the required water horsepower is 6.0 hp, what is the
required brake horsepower?
9. Motor Horsepower
The rated horsepower of the motor necessary to produce the desired brake
and water horsepower.
Example: The motor is 94% efficient. What is the required
motor horsepower when the required brake horsepower is 7.0 Bhp?
10. Electrical Power
To determine the electrical energy required/consumed during a given
period of time, the horsepower is converted to electrical energy, (kilowatts),
then multiplied by the hours of operation to obtain kilowatt hours.
Example: A 50 horsepower motor
operates at full load 12 hours per daily (seven days per week). How
many kilowatt hours of energy does it consume per day?
