Newton's Law of Viscosity gives the relationship between the shear stress and the shear rate or the velocity gradient of a liquid that is subject to a mechanical force.

The law is not universal in its application.  It is applicable to some liquids while other liquids do not obey it.

Newton's Law of Viscosity can be mathematically described as

t =  m dv/dy

where t = shear stress
           dv/dy is the velocity gradient

Liquids which obey Newton's Law of Viscosity are called Newtonian liquids.  Liquids whose response cannot be described by this law are called Non-Newtonian Liquids.

A Newtonian liquid is one in which the viscosity of the liquid is constant regardless of the stress applied.  That is, the viscosity of the liquid is the same if it is left alone or agitated vigorously.

In other words, Newtonian liquids obey Newton's law of viscosity which states that the shear stress is proportional to the rate of strain.

Water is a common example of a Newtonian liquid.  The viscosity of water is same whether it is still or in an agitated state.  In contrast, a solution of water and corn starch will be liquid when still but will become highly viscous when agitated.

Liquids in which the viscosity changes in response to the application of stress are called non-Newtonian liquids.

Rheology is the science of the flow of matter, particularly in the liquid or the semisolid state.  It is a subject of interest when designing pumps.  Rheology can help describe the behaviour of materials such as slurries and pastes.

The term Rheology is formed from two Greek works, "Rheo" for flow and "logia" for study. It is based on the assumption that "everything flows" or "Panta Rei", a statement attributed to Heraclitus, a philosopher in ancient Greece.Rheology can also be described as the study of the behaviour of matter when subject to  a deforming load.

In Rheology, flow is considered to be an irreversible deformation of matter as the original state of the fluid or the semi-solid cannot be attained again.

Rheology has applications in the food industry, in pharmaceuticals and in chemical industries.

Metering pumps are special pumps which are used to deliver a liquid at a specific flow rate in a specific time.  Metering pumps are used for dosing chemicals in industrial processes at a specific quantity.

The quantity and duration is often controlled by a computer.

Metering pumps are positive displacement pumps which can deliver output at high pressures. The pump is usually driven by a piston.

For sensitive liquids which require sterility and for corrosive liquids, the pump is ideal as it does not come in contact with the liquid.  A diaphragm acts as the interface between the piston and the liquid.

Metering pumps can also be designed as gear pumps.

A diaphragm is a special type of pump which uses a diaphragm to create pressure.  The diaphragm pump consists of a container with an inlet and outlet valves.  The top of the container is covered with the diaphragm.

The diaphragm is operated by an external mechanism which moves the diaphragm up and down.  When the diaphragm is pulled up, low pressure is created and the liquid is drawn inside the pump.  When diaphragm is pushed down, the fluid inside is pressurized and released through the outlet valve.

A salient feature of the diaphragm pump is that the fluid does not come in contact with the pump components.  Diaphragm pumps are used in the field of medicine where they can be used to construct artificial hearts and in dialysis.

They are also used widely in the food processing industry.

Another common application is in aquariums.  Aquarium pumps which provide air to aerate aquariums are a type of diaphragm pumps.

Plunger Pumps and Piston pumps work on the same principle.  They both draw a fixed volume of liquid through the inlet and pressurize the liquid and then release the liquid.

The difference lies in the construction.  In Piston pumps, the seal which prevents leakage moves with the piston.  In plunger, the seal is stationary and the plunger alone moves.

This enables the generation of very high pressure.  Plunger pumps can build pressures of the order of MegaPascals.  Plunger Pumps are used in high pressure applications.

A plunger pump is a positive displacement pump.  In a plunger pump, the plunger moves up and down a cylinder.

When the plunger moves up the cylinder, a low pressure is created in the cylinder.  The fluids is drawn by the low pressure by means of non return valves in the inlet of the pump.

When the plunger moves down, the increased pressure closes in the non-return valves in the inlet.  The liquid is pressurized as the plunger moves downwards.  This high pressure opens the outlet valve and the liquid is ejected at high pressure.

Plunger Pumps can be used at high pressure because of their robust and simple design.  

Centrifugal pumps need to be primed separately.  The priming can be manual or through a separate priming arrangments

Positive displacement pumps are self priming as they develop a low pressure which can draw the fluid inside.

Flow Rate
Centrifugal Pumps have a flow rate which is dependent on the discharge pressure

Positive Displacement pumps have a constant flow rate regardless of the pressure

Viscous Fluids
Centrifugal pumps cannot handle viscous fluids due to increased friction between the impeller and the liquid.

Positive displacement pumps can handle viscous fluids.

Centrifugal pumps have lower efficiency as the viscosity increases

Positive displacement pumps have high efficiency as the viscosity increases

Method of operation
Centrifugal pumps build pressure by imparting velocity to the liquid and then converting it into pressure.

Positive displacement pumps develop pressure by drawing a fixed amount of liquid and pressurizing it.

A positive displacement pump is a pump which draws a fixed amount of the liquid from the inlet and discharges it in the outlet at high pressure.

Positive displacement pumps have an expanding cavity in the inlet and a decreasing cavity near the inlet.  Positive displacement pumps have constant volume.  The pumps deliver a constant flow regardless of the discharge pressure.  The pressure depends on the speed of the pump.

Positive displacement pumps can be further classified into reciprocating pumps, rotary pumps, etc.

Positive displacement pumps should never be operated with the outlet closed. Since the pump works on a fixed volume of liquid,  the pump can get seriously damaged if it is accidentally operated with the outlet closed.

A special pressure relief valve is provided for protection against excess pressure.

Cavitation refers to the erosive action on the pump impeller and casing by the explosion of bubbles which form in the medium.

When the liquid passes through the impeller, the pressure drops in certain areas, this causes the liquids to drop below the vapor pressure.  As a result, bubbles are formed.  When these bubbles break, the energy released can remove small amounts of materials from the impeller and the casing.

Cavitation can cause the housing of the pump to fail.  In some instances, it can cause damage to the impeller.  A damaged impeller can get unbalanced and cause high vibration.  The outflow of the pump will also be affected

Cavitation in Pumps is classified into two types

Suction Cavitation
In suction cavitation, inadequate flow into the pump from the suction side due to blocked filters can cause low pressure in the eye of the impeller, this causes bubbles to form.  These bubbles pass to the discharge side where they encounter high pressure.  This causes the bubbles to implode releasing energy which can damage the impeller.

Discharge Cavitation
This occurs due to reduced outflow from the pump.  If the output of the pump is reduced, the pressure increases.  The liquid is unable to exit the pump and recirculates within the pump.  This high speed flow causes a vacuum between the liquid and the wall of the pump housing.  This causes bubbles to form and damage the inner surface of the casing.

In Pump design, shear sensitivity is an important factor.  Shear sensitivity refers to the response of a liquid when the shear forces inside a pump increase.  Shear forces increase as the pump speed increases.

Water is a shear insensitive liquid.  That is, even if the water is stirred fast it does not change its viscosity.  There are substances in which the viscosity of the liquid changes when shear forces are applied.

Viscosity is a fundamental property of the liquid.  The change in viscosity can affects other processes.  Hence, when pumps is selected, the shear sensitivity of the liquid should also be kept in mind.

Shear sensitive liquids are pumped using low speed pumps where the shear is minimal.

Centrifugal pumps are used widely to pump liquids such as water.  They cannot be used to pump viscous liquids.

The high viscosity of the liquid will cause increased friction losses between the impeller and the liquid.  The friction losses result in reduced head and the pump efficiency reduces.  There is a sharp reduction in the pump flow as the viscosity of the medium increases.

Besides, the flow inside the pump will not be streamlined and this increases the losses and loading in the impeller.

Hence, the centrifugal pump cannot be used to pump viscous liquids.  Viscous fluids are pumped by positive displacement pumps.

Velocity head is the difference in velocity of the liquid at the suction nozzle and the discharge nozzle.  This difference in velocity is caused by difference in the size of the nozzles.

If the discharge nozzle is smaller than the suction nozzle, the water will exit at a higher speed at the discharge nozzle than at the suction nozzle.

This difference in velocities creates a head.  This head is known as the Velocity Head in Pumps.  If the discharge and the suction nozzles are of equal size, the velocity head is zero.

Suction Head
The suction head refers to the difference in level between the water  in the sump to the centre line of the pump.  It is expressed in metres

The Delivery head
The Delivery head is the difference in level from the water level in the tank to the centre line of the pump.  It is expressed in metres

Static head
The difference between the water level of the tank to the water level of the sump when the pump is not running is called the Static head.  Its unit is metres.

The centrifugal pump is not self-priming.  The pump needs to be primed before it can function.  Priming involves filling the pump casing with water and removing the air inside.

When the centrifugal pump is started for the first time, the casing should be filled with water until it is filled completely, the delivery valve should be closed and the pump should be started.  When sufficient pressure is built, the delivery valve can be gradually opened.

Priming can be done manually for the first time by means of special openings provided in the pump to fill water.  For subsequent start ups, special arrangements can be made such as having a footer valve in the suction pipe.  This ensures that the pump remains flooded even when it is not running. Another method is to have a separate smaller pump to remove the air in the main pump.

In some installations, the pump is placed at lower level than the sump so that the pump is always flooded.

The centrifugal pump consists of the following main parts.

The Impeller
The Impeller is the heart of the pump.  The impeller provides kinetic energy to the water entering the pump from the suction pipe.

The Volute
The volute refers to the tubular casing of the pump which increases in size as it approaches the discharge port.  The function of the volute is to convert the velocity of the water from the impeller into pressure.  It achieves this by a gradual increase in volume.

The Suction Pipe
The Suction pipe connects the sump to the pump inlet.

The Foot Valve
The foot valve is a non-return valve which is connected on the suction side.  The foot valve prevents the flow of water from the overhead tank which is at a higher level to the sump when the pump is not running.

The Strainer
The Strainer prevents the entry of debris into the pump

The Delivery Pipe
The Delivery Pipe serves to supply water to the tank from the discharge side of the pump.

The Delivery Valve
The delivery valve is a valve at the output of the pump in the delivery line.  The function of this valve is to control the output of the pump.  The delivery valve is closed when the pump is first started during the priming process.  It is then gradually opened.

A Diffuser pump is on in which stationary vanes called diffusers are fitted radially facing the discharge from the impeller.  These vanes which gradually increase in space as the water moves outwards serve to convert the velocity of the water exiting the impeller into pressure.

Diffuser pumps do not require a volute.  Diffuser pumps provide a more efficient conversion of velocity input pressure.  The flow is more controlled and smoother.

For large capacity pumps, the diffuser model is smaller in size than the volute design.

The diffuser design is more efficient at peak loads while the volute design is efficient at off peak loads.

The Hydraulic Efficiency of a pump is the ratio of the useful hydrodynamic energy in the fluid to the energy supplied to the rotor of the pump.

Hydraulic Efficiency = Useful hydrodynamic Energy / Energy Supplied to the Rotor of the pump

The hydraulic efficiency is related to the number of vanes in centrifugal pumps and the depth of the channels. Optimizing the design of the impeller such that the friction between the liquid and the impeller surface is minimum can also improve hydraulic efficiency.

The Volumetric Efficiency of a Pump refers to the ratio of the total ouput of the pump to the total output of the pump without losses.

It can also be described as the ratio of the theoretical flow of the pump to the actual flow.  The theoretical flow of the pump can be calculated from the pump design data.  The theoretical flow of the pump is the product of the displacement per revolution and the number of revolutions.

The actual flow is measured by a flow meter which is connected to the pump output.

For instance if the displacement per revolution of a pump is 120cc/ rev and the pump has a speed of 1000 rpm, the theoretical flow rate would be 120x1000 = 120000cc or 120 litres per minute.

If the actual flow measured is around 115 litres per minute, the volumetric efficiency of the pump can be calculated as (115/120) x 100 = 95%

The volumetric efficiency can be reduced by reducing the leakages from the pump.

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