Pumps, Fans and Turbines  Horsepower
British Horse Power as used for pumps, fans and turbines  and how to convert to other units.
Horsepower
Horsepower is the imperial (British) unit of power. A horsepower is the ability to do work at the rate of
 33000 ft.lb per min or
 550 ft.lb per second
Note that Power is "Work per unit time" and work is "Force through distance". In gravity systems the Force is Weight  mass multiplied with gravity.
In the SI system the unit of power is watt (W, Nm/s, J/s).
The total horsepower developed by water falling from a given height is the product of the mass flow rate in pounds per minute times the falling height in feet divided by 33000 and can be expressed as:
P_{hp} = m_{min} h a_{g} / 33000 (1)
where
P_{hp} = power (horsepower, hp)
m_{min} = mass flow rate per minute (lb_{m}/min)
h = head or height (ft)
a_{g} = acceleration of gravity (32 ft/s^{2})
(1) can alternatively be expressed as:
P_{hp} = m_{sec} h a_{g} / 550 (1b)
where
m_{sec} = mass flow rate per second (lb_{m}/s)
(1) can also be expressed as:
P_{hp} = γ Q h / 33000 (1c)
where
Q = volume flow rate (ft^{3}/min)
γ= specific weight (lb_{f}/ft^{3}) (weight is force)
Water Horsepower for Flow in gal/min
Water horsepower for flow in gal/min can be expressed as:
P_{whp} = SG Q_{gal} h / 3960 (1d)
where
Q = volume flow rate (gpm)
SG= specific gravity
h = head (ft)
SG for water is 1.001 at 32^{o}F and 0.948 at 240^{o}F.
Power to Pump Water
Required horsepower (hp) to pump 1 cubic foot of water per minute (ft^{3}/min) with efficiency 85%  is indicated in the diagram below:
 1 hp (English horse power) = 745.7 W
 1 ft (foot) = 0.3048 m
Example  Required Power to lift 10 ft^{3}/min of Water 600 ft
According the diagram above 1 hp is required to lift 1 ft^{3}/min of water 600 ft. Required power to pump 10 ft^{3}/min can be calculated as
(10 ft^{3}/min) (1 hp) / (1 ft^{3}/min) = 10 hp
Shaft or Brake Horsepower
The brake horsepower is the amount of real horsepower going to the pump, not the horsepower used by the motor. In the metric system kilowatts (kW) is used.
Due to hydraulic, mechanical and volumetric losses in a pump or turbine the actual horsepower available for work on or from the fluid is less than the total horsepower supplied.
Shaft or Brake Horsepower for a Pump or Fan
The brake horse power  bhp  for a pump or fan can be expressed as:
P_{bhp} = ( γ Q h / 33000 ) / η (2)
where
P_{bhp} = brake horse power (horsepower, hp)
Q = volume flow rate (ft^{3}/min, cfm)
Shaft or Brake Horsepower for a Turbine
The brake horse power  bhp  for a turbine can be expressed as:
P_{bhp} = η ( γ Q h / 33000 ) (2b)
Input Horsepower to the Electrical Motor
The input horsepower to the electrical motor for a pump or fan can be expressed as:
P_{hp_el} = P_{bhp} /η_{e} (3)
or
P_{hp_el} = (m h g / 33000) / (ηη_{e}) (3b)
where
P_{hp_el} = input power to the electrical motor
η_{e} = mechanical efficiency of the electrical motor
Horsepower in Kilowatts and other Units
Horsepower can be converted to other common units as:
 1 hp (English horse power) = 745.7 W = 0.746 kW = 550 ft.lb/s = 2545 Btu/h = 33000 ft.lb/m = 1.0139 metric horse power
Transforming horsepower to kW:
P_{kW} = 0.746 P_{hp} (4)
where
P_{kW} = power (kW)
Together with the equations above it's possible to express (4) in many common combinations  such as:
P_{kW} = 0.746 (m h / 33000) / η η_{e} (5)
Example  Pump Power
The horsepower required to pump 50 lb_{m}/min water a head of 10 ft with a pump with overall efficiency 0.7  can be calculated with eq. (3) as
P_{hp} = ((50 lb_{m}/min)(10 ft) (32 ft/s^{2}) / 33000) / 0.8
= 0.6 hp
The power in kW can be calculated as
P_{kW} = 0.746 (0.6 hp)
= 0.45 kW
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