POWER AND EFFICIENCY OF CENTRIFUGAL PUMP

Power and efficiency of centrifugal pump
Brake Horse Power (BHP) and Water horsepower (WHP)

• The work performed by a pump is a function of the total head and the weight of the liquid pumped in a given time period.

Pump input or brake horsepower (BHP) is the actual horsepower delivered to the pump shaft.

Pump output or hydraulic or water horsepower (WHP) is the liquid horsepower delivered by the pump.

• These two terms are defined by the following formulas.

where

• Q = Capacity in gallons per minute (GPM)
• HT = Total differential head, ft
• Specific gravity= Specific gravity of liquid
• Efficiency = Pump efficiency, %

• The constant 3960 is obtained by dividing the number or foot-pounds for one horsepower(33,000) by the weight of one gallon of water (8.33 pounds). 

The brake horsepower or input to a pump is greater than the hydraulic horsepower or output due to the mechanical and hydraulic losses incurred in the pump.

• Therefore the pump efficiency is the ratio of these two values.

Best Efficiency Point (BEP)

• The Head, NPSHr, efficiency, and BHP all vary with flow rate, Q.

Best Efficiency Point (BEP) is the capacity at maximum impeller diameter at which the efficiency is highest.

Significance of BEP

• BEP as a measure of optimum energy conversion
• When sizing and selecting centrifugal pumps for a given application the pump efficiency at design should be taken into consideration.
• The efficiency of centrifugal pumps is stated as a percentage and represents a unit of measure describing the change of centrifugal force (expressed as the velocity of the fluid) into pressure energy.
• The B.E.P.(best efficiency point) is the area on the curve where the change of velocity energy into pressure energy at a given gallon per minute is optimum; in essence, the point where the pump is most efficient.
• The operation of a centrifugal pump should not be outside the furthest left or right efficiency curves published by the manufacturer.
• Performance in these areas induces premature bearing and mechanical seal failures due to shaft deflection, and an increase in temperature of the process fluid in the pump casing causing seizure of close tolerance parts and cavitation.
• BEP is an important parameter in that many parametric calculations such as specific speed, suction specific speed, hydrodynamic size, viscosity correction, head rise to shut-off, etc. are based on capacity at BEP.
• Many users prefer that pumps operate within 80%to 110% of BEP for optimum performance.

Specific Speed

Specific speed as a measure of the geometric similarity of pumps

• Specific speed (Ns) is a non-dimensional design index that identifies the geometric similarity of pumps.
• It is used to classify pump impellers as to their type and proportions.
• Pumps of the same Ns but of different size are considered to be geometrically similar,one pump being a size- factor of the other.

Specific speed Calculation

• The following formula is used to determine specific speed:

where

• Q = Capacity at best efficiency point(BEP) at maximum impeller diameter, GPM(gallons per meter)
• H = Head per stage at BEP at maximum impeller diameter, ft
• N = pump speed, RPM

• As per the above formula, it is defined as the speed in revolutions per minute at which a geometrically similar impeller would operate if it were of such a size as to deliver one gallon per minute flow against one-foot head.
• Specific speed should be thought of only as an index used to predict certain pump characteristics.
• The specific speed determines the general shape or class of the impellers.

NET POSITIVE SUCTION HEAD

Net Positive Suction Head (NPSH)

• Power supplied to the pump depend on the difference in the pressure between discharge and suction and is independent of the pressure level.
• There is no effect on pump when suction pressure is below atmospheric pressure or well above it, as long as the fluid remains liquid.
• But if suction pressure is only slightly greater than the vapor pressure, some liquid may flash to vapor inside to pump, a process called cavitation, which greatly reduces the pump capacity.
• If the suction pressure is actually less than the vapor pressure, there will be vaporization in the suction line, and no liquid can be drawn into the pump.
• To avoid cavitation, the pressure at the pump inlet must exceed the vapor pressure by certain value called net positive suction head (NPSH)

Hence, Net Positive Suction Head or NPSH for pumps can be defined as the difference between liquid pressure at pump suction and liquid vapor pressure, expressed in terms of height of liquid column.

• Net positive suction head (NPSH) may refer to one of two quantities in the analysis of cavitation.

1. The Available NPSH (NPSHA): A measure of how close the fluid at a given point is to flashing, and so to cavitation.
2. The Required NPSH (NPSHR): The head value at a specific point (e.g. the inlet of a pump) required to keep the fluid from cavitating.

Net Positive Suction Head Required, NPSHr

• Pumps can pump only liquids, not vapors
• The satisfactory operation of a pump requires that vaporization of the liquid being pumped does not occur at any condition of operation.
• This is so desired because when a liquid vaporizes its volume increases very much.
• For example, 1 ft3 of water at room temperature becomes 1700 ft3 of vapor at the same temperature.
• This makes it clear that if we are to pump a fluid effectively, it must be kept always in the liquid form.
• Rise in temperature and fall in pressure induces vaporization
• The vaporization begins when the vapor pressure of the liquid at the operating temperature equals the external system pressure, which, in an open system is always equal to atmospheric pressure.
• Any decrease in external pressure or rise in operating temperature can induce vaporization and the pump stops pumping.
• Thus, the pump always needs to have a sufficient amount of suction head present to prevent this vaporization at the lowest pressure point in the pump.
• NPSH as a measure to prevent liquid vaporization
• NPSH required is a function of the pump design and is determined based on actual pump test by the vendor.
• NPSHr increases as capacity increases
• The NPSH required varies with speed and capacity within any particular pump.
• The NPSH required increase as the capacity is increasing because the velocity of the liquid is increasing, and as anytime the velocity of a liquid goes up, the pressure or head comes down.
• The NPSH is independent of the fluid density as are all head terms.

Net Positive Suction Head available, NPSHa

• Net Positive Suction Head Available is a function of the system in which the pump operates.
• It is the excess pressure of the liquid in feet absolute over its vapor pressure as it arrives at the pump suction, to be sure that the pump selected does not cavitate.
• It is calculated based on system or process conditions.
• The formula for calculating the NPSHa is as below

where

hps= pressure head i. e. absolute pressure at surface of reservoir converted into head
hs= static suction head
hvps= vapor pressure head
hfs= friction head 

Significance of NPSHr and NPSHa

• The NPSH available must always be greater than the NPSH required for the pump to operate properly.

PERFORMANCE PARAMETER OF CENTRIFUGAL PUMP

Performance parameter of centrifugal pump
The key performance parameters of centrifugal pumps are 

1. Capacity
2. Head
3. BHP(Brake horse power)
4. BEP (Best efficiency point)
5. Specific speed

Capacity

Capacity means the flow rate with which liquid is moved or pushed by the pump to the desired point in the process. 

• It is commonly measured in either gallons per minute(gpm) or cubic meters per hour (m3 /hr). 
• The capacity usually changes with the changes in operation of the process. 
• The capacity depends on a number of factors like: 

1. Process liquid characteristics i.e. density, viscosity 
2. Size of the pump and its inlet and outlet sections 
3. Impeller size 
4. Impeller rotational speed RPM 
5. Size and shape of cavities between the vanes 
6. Pump suction and discharge temperature and pressure conditions

• The effect on the flow through a pump by changing the outlet pressures is graphed on a pump curve.
• As liquids are essentially incompressible, the capacity is directly related with the velocity of flow in the suction pipe. 
• This relationship is as follows:

where

• Q= capacity
• V = velocity of flow
• A = area of pipe

Head

The pressure at any point in a vertical column of the liquid can be caused due to its weight. The height of this column is called the static head and is expressed in terms of feet of liquid. 

• The same head term is used to measure the kinetic energy created by the pump.

In other words, head is a measurement of the height of a liquid column that the pump could create from the kinetic energy imparted to the liquid. 

• The head is not equivalent to pressure. 
• Head is a term that has units of a length or feet and pressure has units of force per unit area or pound per square inch. 
• The main reason for using head instead of pressure to measure a centrifugal pumps energy is that the pressure from a pump will change if the specific gravity (weight) of the liquid changes, but the head will not change. 
• Since any given centrifugal pump can move a lot of different fluids, with different specific gravities, it is simpler to discuss the pumps head and forget about the pressure.
• A given pump with a given impeller diameter and speed will raise a liquid to a certain height regardless weight of the liquid. 

Pressure to Head Conversion formula 

• The static head corresponding to any specific pressure is dependent upon the weight of the liquid according to the following formula

There are different type of head, which are as follows


1. Static Suction Head (hS ) :

Head resulting from elevation of the liquid relative to the pump centerline is called static suction head. 

• If the liquid level is above pump centerline, hS is positive. 
• If the liquid level is below pump centerline, hS is negative. 
• Negative hS condition is commonly denoted as a “suction lift” condition 

2. Static Discharge Head (hd):

It is the vertical distance in feet between the pump centerline and the point of free discharge or the surface of the liquid in the discharge tank.

3. Friction Head (hf):

This head required to overcome the resistance to flow in the pipe and fittings. 

• It is dependent upon the size, condition and type of pipe, number and type of pipe fittings, flow rate, and nature of the liquid.

3. Vapor Pressure Head (hvp):

• Vapor pressure is the pressure at which a liquid and its vapor co-exist in equilibrium at a given temperature. 

When the vapor pressure is converted to head, it is referred to as vapor pressure head, hvp. 

• The value of hvp of a liquid increases with the rising temperature and in effect, opposes the pressure on the liquid surface, the positive force that tends to cause liquid flow into the pump suction i.e. it reduces the suction pressure head.

4. Pressure Head (hp):

Pressure Head must be considered when a pumping system either begins or terminates in a tank which is under some pressure other than atmospheric. 

• The pressure in such a tank must first be converted to feet of liquid. 
• Denoted as hp, pressure head refers to absolute pressure on the surface of the liquid reservoir supplying the pump suction, converted to feet of head. 
• If the system is open, hp equals atmospheric pressure head.

5. Velocity Head (hv):

Velocity head refers to the energy of a liquid as a result of its motion at some velocity ‘v’. 

• It is the equivalent head in feet through which the water would have to fall to acquire the same velocity, or in other words, the head necessary to accelerate the water. 
• The velocity head is usually insignificant and can be ignored in most high head systems.
• However, it can be a large factor and must be considered in low head systems.

6. Total Suction Head (HS ):

• The suction reservoir pressure head (hpS ) plus the static suction head (hS ) plus the velocity head at the pump suction flange (hVS) minus the friction head in the suction line (hfS ). 

HS = hpS + hS + hvS – hfS 

The total suction head is the reading of the gauge on the suction flange, converted to feet of liquid.

7. Total Discharge Head (Hd):

• The discharge reservoir pressure head (hpd ) plus static discharge head (hd) plus the velocity head at the pump discharge flange (hvd ) plus the total friction head in the discharge line (hfd). 

Hd = hpd + hd + hvd + hfd 

The total discharge head is the reading of a gauge at the discharge flange, converted to feet of liquid. 

8. Total Differential Head (HT):

It is the total discharge head minus the total suction head  

HT = Hd + HS (with a suction lift) 

HT = Hd - HS (with a suction head)