Pumps Terminilogies

The System Curve

A fluid flow system can in general be characterized with the System Curve - a graphical presentation of the Energy Equation.

The system head visualized in the System Curve is a function of the elevation - the static head in the system, and the major and minor losses and can be expressed as:

h = dh + h_l         (1)

where

h = system head

dh = h₂ - h₁ = elevation (static) head - difference between inlet and outlet of the system

h_l = head loss

A generic expression of head loss is:

h_l = k q²         (2)

where

q = flow rate

k = constant describing the total system characteristics - including all major and minor losses

Increasing the constant - k - by closing some valves, reducing the pipe size or similar - will increase the head loss and move the system curve upwards. The starting point for the curve - at no flow, will be the same.

Pump Performance Curve

The pump characteristic is normally described graphically by the manufacturer as a pump performance curve. The pump curve describes the relation between flowrate and head for the actual pump. Other important information for proper pump selection is also included - efficiency curves, NPSH_r curve, pump curves for several impeller diameters and different speeds, and power consumption.

Increasing the impeller diameter or speed increases the head and flow rate capacity - and the pump curve moves upwards.

The head capacity can be increased by connecting two or more pumps in series, or the flow rate capacity can be increased by connecting two or more pumps in parallel.

Selection of Pump

A pump can be selected by combining the System Curve and the Pump Curve

The operating point is where the system curve and the actual pump curve intersect.

Best Efficiency Point - BEP

The best operating conditions will in general be close to the best efficiency point - BEP.

Special consideration should be taken for applications where the system conditions change frequently during operation. This is often the situation for heating and air conditioning system or water supply systems with variable consumption and modulating valves.

Carry Out

When a pumps operates in the far right of its curve with poor efficiency - the pumps carry out.

Shutoff Head

Shutoff head is the head produced when the pump operates with fluid but with no flow rate.

Churn

A pump is in churn when it operates at shutoff head or no flow.

Pumps in Serial - Heads Added

When two (or more) pumps are arranged in serial, their resulting pump performance curve is obtained by adding their heads at same flow rate as indicated in the figure below.

Centrifugal pump in series are used to overcome larger system head loss than one pump can handle alone. For two identical pumps in serie the head will be twice the head of a single pump at the same flow rate. With constant flowrate the combined head moves from 1 to 2. In practice the combined head and flow rated moved along the system curve to 3.
If one of the pumps stops, the operation point moves allong the system resistance curve from point 1 to point 2 - head and flow rate are decreased.
 Series operation of single stage pumps is seldom encountered - more often multistage centrifugal pumps are used. 

Pumps in Parallel - Flow Rate Added

When two or more pumps are arranged in parallel their resulting performance curve is obtained by adding their flowrates at the same head as indicated in the figure below.

Centrifugal pumps in parallel are used to overcome larger volume flows than one pump can handle alone. For two identical pumps in parallel the flowrate will double (moving from 1 to 2) compared to a single pump if head is kept constant. In practice the combined head and volume flow moves along the system curve as indicated from 1 to 3.
If one of the pumps in parallel or series stops, the operation point moves along the system resistance curve from point 3 to point 1 - the head and flow rate are decreased.

TEMPERATURE RISE IN PUPMS

No pump is perfect with 100% efficiency. The energy lost in friction and hydraulic losses are transformed to heat - heating up the fluid transported through the pump.

The temperature rise can be calculated as
dt = P_s (1 - μ) / c_p q ρ          (1)
where
dt = temperature rise in the pump (^oC)
q = volume flow through the pump (m³/s)
P_s = brake power (kW)
c_p = specific heat capacity of the fluid (kJ/kg^oC)
μ = pump efficiency
ρ = fluid density (kg/m³)


Typical relation between the centrifugal pump flow, efficiency and power consumption, is indicated in the figure below:

Example - Temperature rise in water pump

The temperature rise in a water pump working at normal conditions with flow 6 m³/h (0.0017 m³/s), brake power 0.11 kW and pump efficiency of 28% (0.28), can be calculated as


dt = (0.11 kW) (1 - 0.28) / (4.2 kJ/kg^oC) (0.0017 m³/s) (1000 kg/m³)


    = 0.011 ^oC


If the flow of the pump is reduced by throttling the discharge valve, the temperature rise through the pump will increase. If the flow is reduced to 2 m³/h (0.00056 m³/s), the brake power is slightly reduced to 0.095 kW and pump efficiency reduced to 15% (0.15), the temperature rise can be calculated as


dt = (0.095 kW) (1 - 0.15) / (4.2 kJ/kg^oC) (0.00056 m³/s) (1000 kg/m³)


    = 0.035 ^oC


With the standard documentation provided by a manufacturer it should be possible to express the temperature rise as a function of volume flow as shown in the figure below:

Hydraulic Pump Power

The ideal hydraulic power to drive a pump depends on the mass flow rate, the liquid density and the differential height.

- either it is the static lift from one height to an other, or the friction head loss component of the system - can be calculated as


P_h = q ρ g h / (3.6 10⁶)            (1)


where


P_h = power (kW)
q = flow capacity (m³/h)
ρ = density of fluid (kg/m³)
g = gravity (9.81 m/s²)
h = differential head (m)

Shaft Pump Power

The shaft power - the power required transferred from the motor to the shaft of the pump - depends on the efficiency of the pump and can be calculated 


as


P_s = P_h / η            (2)


where


P_s = shaft power (kW)
η = pump efficiency

Horsepower

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)

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^oF and 0.948 at 240^oF.