Pumps, Fans and Turbines - Horsepower

[Esam]

[h=Horsepower]3[/h] Horsepower is the imperial (British) unit of power. A horsepower is the ability to do work at the rate of

• 33,000 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 Force is Weight - mass multiplied with gravity.
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 33,000. It can be expressed as:

P_hp = m_min h g / 33000 (1)
where

P_hp = power (horsepower, hp)
m_min = mass flow rate per minute (lb_m/min)
h = head or height (ft)
g = acceleration of gravity (32 ft/s²)

(1) can alternatively be expressed as:

P_hp = m_sec h 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 (ft³/min)
γ = specific weight (lb_f/ft³) (weight is force)

[h=Water Horsepower for Flow in gal/min]4[/h] 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^oF and 0.948 at 240^oF.


[h=Horsepower due to Certain Head of Water]3[/h] Horsepower of 1 cubic foot of water per minute - efficiency 85%.

[h=Shaft or Brake Horsepower]3[/h] 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.
[h=Shaft or Brake Horsepower for a Pump or Fan]4[/h] 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 (ft³/min, cfm)
η = overall efficiency

[h=Shaft or Brake Horsepower for a Turbine]4[/h] The brake horse power - bhp - for a turbine can be expressed as:

P_bhp = η ( γ Q h / 33000 ) (2b)

[h=Input Horsepower to the Electrical Motor]3[/h] 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 / 33000) / (η η_e) (3b)
where
P_{hp_el} = input power to the electrical motor
η_e = mechanical efficiency of the electrical motor

[h=Horsepower in Kilowatts and other Units]3[/h] 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 kiloWatt can be expressed as:

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 as:

P_kW = 0,746 (m h / 33000) / η η_e (5)

[Esam]

Significant differences between pumps, compressors, blowers and fans are summarized below
[h=Pumps]3[/h]

• A pump is a machine for raising a liquid - a relatively incompressible fluid - to a higher level of pressure or head.

[h=Compressors]3[/h]

• A compressor is a machine for raising a gas - a compressible fluid - to a higher level of pressure.

[h=Blowers]3[/h]

• A blower is a machine for moving volumes of a gas with moderate increase of pressure.

[h=Fans]3[/h]

• A fan moves large amounts of gas with low increase in pressure.