Newtonian and Non-Newtonian Fluids, Water Hammering, and Cavitation in Pumps

While handling pumping systems, it is critical to have a background understanding of some of the important concepts that govern pump performance, efficiency, output, and longevity. The following resource aims to discuss the concepts of Newtonian/Non-Newtonian fluids, water hammering, cavitation in pumps, and how these factors impact modern pumping systems.

Newtonian and Non-Newtonian fluids

In fluid pumping, it is fairly important to understand the properties of the fluids being pumped, transferred, and mixed. This understanding plays a major role in selecting suitable equipment for fluid pumping. Fluid viscosity or thickness determines the way a particular fluid will behave in a pump. When it comes to fluid viscosity, fluids show a non-uniform pattern. Some fluids maintain a constant viscosity while others show a significant change in viscosity as temperature and applied forces change. 

In general, fluids can be divided into two broad categories. Newtonian fluids and Non-Newtonian fluids. Non-Newtonian fluids have further subcategories (more on that later). Pump manufacturers and end-users must have a clear understanding of these fluid types and their behavior. This plays a vital role while selecting and operating pumps.

Understanding ‘Shear’

Before we move on, it is important to understand the concept of ‘shear’. In very simple terms, shear is the relative motion between adjacent layers of a fluid that is in motion. An example of a fluid in motion is when butter is applied to bread. In this case, there is relative motion between two layers of fluid (butter on the knife and butter on the bread). 

In the case of solids, the shear force acts tangentially to the surface of the solid. A solid can resist deformation due to this force but a fluid will flow under its influence. When adjacent layers of a fluid move relative to each other, shear stresses are developed. Shear forces are developed because adjacent layers of a fluid move with different velocities in a pipe (thus there is relative motion between them). Shear rate is defined as a measure of the extent of this relative motion between the layers.

Newtonian Fluids

Newton’s law states that the shear stress is directly proportional to shear rate when fluid viscosity is constant. Fluids obeying this law are called Newtonian fluids. In other words, the fluid viscosity does not change no matter how much shear is experienced by it. In the case of Newtonian fluids, kinematic viscosity is considered. This is the viscosity when no external forces are acting on the fluid. In other words, this is the viscosity when only gravity is acting upon a fluid. The kinematic viscosity of Newtonian fluids remains constant even if external forces are applied to the fluid. Examples of such fluids include water, high viscosity fuel, some motor oils, most mineral oils, gasoline, kerosene, most salt solutions in water, light suspensions of dye stuff, kaolin (clay slurry). These fluids have fairly defined and consistent flow characteristics.

Non-Newtonian Fluids

The viscosity of these fluids changes as shear is applied. This makes them much more challenging to pump. In the case of Non-Newtonian fluids, the Dynamic viscosity is considered and it changes when shear is experienced by the fluid. During pump design, the changing viscosity has to be considered for ensuring appropriate flow, pipe size, and optimum pump characteristics (pump speed; inlet pressure requirements; pump pressure drop to initiate flow). Depending upon how the viscosity changes in response to external forces, Non-Newtonian fluids are further divided into sub-categories. These categories are as follows:

Dilatant

The fluid viscosity increases as shear is applied. They are also called shear thickening. If you quickly try to force an object through such a fluid, it will be met with a lot of resistance. On the contrary, slowly introducing the object will give its molecules the time to move away and the object will move while facing much less resistance. Examples of such liquids include:

• Feldspar 
• Quicksand 
• Beach sand 
• Clay
• Mica
• Silly putty 

Figure 1: Stress response of dilatants and pseudoplastics

Thixotropic

In addition to shear, the viscosity is also time-dependent in the case of thixotropic fluids. The application of shear decreases the viscosity and the viscosity also decreases as time goes by. These fluids include:

• Silica gel 
• Greases
• Bentonite
• Inks
• Mayonnaise

Figure 2: Stress response of Rheopectic and thixotropic fluids

Shear thickening in pumps

As discussed earlier, Non-Newtonian shear-sensitive fluids change in viscosity in response to shear. This means that while passing through the impeller of a pump, the fluid viscosity changes in response to forces exerted by the impeller. Shear thickening fluids (dilatants) increase in viscosity while the viscosity of shear-thinning fluids decreases when forces are applied. Corn starch, for example, is a dilatant, and its viscosity increases when a mixture of cornstarch and water flows out of a pump.

Why are high efficiency pumps important?

Pump efficiency is the ratio of the amount of fluid entering the pump to the amount of fluid leaving it. A pump with higher pump efficiency is more effective for gentle product handling. A low-efficiency pump means that some portion of the product remains in the pump casing and is recirculated. This further impacts the fluid’s viscosity and sometimes the changes in viscosity can be permanent due to overhandling which can result in compromising the product’s integrity. 

To avoid this problem, a positive displacement pump can be used. Such a pump can deliver a constant flow rate at a given pump speed. Even if the viscosity increases, a constant rate of the fluid can be dispensed by ramping up the pump’s horsepower.

Water Hammer and its causes

Water hammer is a surge of pressure that can arise in pumping systems. The pressure is created when the pumping system undergoes an abrupt change in flow. The main causes of water hammering include opening and closing of valves, pump starts and stops, and separation and closure of the water columns. Due to these factors, the water column undergoes a change in momentum and this abrupt change can produce shock waves that travel back and forth within the system. Depending on the magnitude of the shock wave, physical damage in the system can be severe. 

The phenomenon can be understood by an example in which water is pumped in a pipe that has valves on its both ends. The inlet valve is opened and the water column starts traveling towards the discharge valve. At this point, the discharge valve is closed instantly and the leading edge of the water column strikes the closed valve and begins to compress. A pressure wave (shock wave) begins to travel along the backstream (towards the inlet valve). The shock wave travels back and forth between the two valves until it finally diminishes due to friction losses. This water hammer shock wave is so fast that it can make a round trip between the two valves in less than half a second in the case of a 1000 feet pipe. The pressure created by this shock wave depends on the wave velocity (a), the velocity of water in the pipe (V), and the universal gravitational constant (g). Mathematically,

P = a V / 2.31 g

Even at a pipe velocity of just 10 ft/sec, the additional pressure can reach 657 psi. This is a huge amount of pressure that can easily devour pipelines! 

Causes of water hammer

If we examine the causes of this phenomenon, there appear to be three dominant factors:

• Valve opening and closure
• Pump start and stops
• Water column separation and closure

Figure 3.

If the valve is closed quickly when the water is flowing in the branch line, a shock wave will develop and will travel back and forth between the valve and the Tee. The time of valve closure (i.e. how quickly the valve is closed) also affects the intensity of the water hammer. The following equation gives the relationship between the additional pressure generated by the shock wave (P), flow velocity in ft/sec (V), pipe length between barriers (P), and valve closing time in seconds (t): 

P = 0.07 (VL / t)

The additional pressure is directly related to the flow velocity and length of the pipe between the barriers. It is inversely related to the valve closure time. Since the pipe length is often fixed, the additional pressure caused by the water hammer can be managed by changing the valve closure timing and the flow velocity. 

It is also important to know that water hammering can have more devastating effects in systems designed to operate at low pressures. A 1000 ft pipe with a 5 ft/s flow velocity will experience the same intensity of shockwave whether operating at a pressure of 50 psi or operating at a pressure of 200 psi. The main difference is that the ratio of shock pressure to design pressure will be much higher for a system with a 50 psi design pressure than for a system with a 200 psi design pressure. The damage in the case of the 50 psi system will, therefore, be much greater.

Pump starts and stops

When a pump is started in large pumping systems, it is done so when the discharge valve is closed. The valve is opened slowly only after the pump has reached its maximum speed. Water hammer is significantly reduced when the pumps are started and stopped against a valve that is opened or closed slowly. 

The problem occurs when the pump motor loses power during a power outage. This reduces the water flow at pump discharge and a water hammer is created due to abrupt changes in pressure and kinetic energy of the flowing water. This shockwave can reverse the water direction that can prompt the pump impeller to accelerate in the reverse direction. This creates additional pressure because backflow is reduced when the impeller reaches maximum reverse speed. 

To mitigate this situation, a ‘spring-loaded’ check valve is installed at the pump discharge and a specific value of pressure is maintained at the pump inlet. When the pump starts, it has to create more pressure than that at the pump inlet in order for the flow to initiate. This ensures that the flow is increased gradually and water hammering is not initiated. When the pump stops, the spring-loaded valve is instantly closed. This prevents the water column from changing direction and a relatively uniform pressure is maintained through the pipeline. 

If a normal check valve is used instead of a spring-loaded one, the water column will accelerate backward and slam the check valve close thus initiating a shock wave.

Water column closure and separation

This occurs in a two-phase system when the water column exists as liquid and vapor simultaneously. When the pressure in the pipeline is reduced below the vapor pressure of water, a phase change can occur. This can separate portions of the liquid water column by creating pockets of water vapor in between. When the pressure rises and exceeds vapor pressure, the liquid water column joins again (water column closure) that can create a wave of high pressure. This is how water column closure and separation can cause damage to thin-walled pipes.

Cavitation in pumps

When the liquid turns to vapor at low pressure, cavitation occurs in pumps. It happens due to a lack of sufficient pressure at the suction end of the pump or insufficient Net Positive Suction Head (NPSH is the difference between the pressure available at the pump inlet and the vapor pressure of the liquid). Cavitation occurs when the pressure and temperature of the liquid at the suction side of the impeller equals the vapor pressure. This creates air bubbles at low pressure. When the liquid travels from the suction side of the impeller to the delivery side, these air bubbles collapse. The force generated when the bubbles implode is often strong enough to damage pump components, seals, shafts, bearings, and impellers. Cavitation can also cause vibration that causes mechanical damage and thus the service life of pumps is reduced.

Why does cavitation occur?

Under normal conditions, liquids have a predictable and steady vapor pressure. When the pressure inside the pump falls below the vapor pressure, cavitation occurs. This drop in pressure is often caused by disruptions in flow. Disruptions in flow can be caused by:

• Poorly specified pump
• Higher than expected viscosity
• Clogged inlet
• Clogged filters and strainers

In addition, at very high discharge pressures, a portion of fluid cannot discharge from the pump. The undischarged fluid gets trapped between the impeller blades and can cause a pressure drop at high velocity. This pressure drop triggers cavitation.

Recognizing pump cavitation

Typical signs of cavitation include:

• Vibration
• Impeller erosion
• Noise
• High power consumption
• Seal or bearing failure

Cavitation usually sounds like gravel or marble moving inside the pipe, pump, or hoses. 

NPSHa and NPSHr

A clear understanding of the NPSHa and NPSHr is critical for understanding the cavitation process. The NPSHa (Net Positive Suction Head Available) is a system-specific value and doesn’t depend on the pump. It is the difference between the pressure at the pump inlet flange and the vapor pressure of the liquid. In short, the head available at the pump suction flange pipework connection is the NPSHa. 

NPSHa = Pressure at pump inlet – vapor pressure

The NPSHr (Net Positive suction Head Required) is not related to the system and is a purely pump specific property. It is the minimum pressure at the pump suction port that will prevent the pump from cavitating. The NPSHr alone is not sufficient to keep the pump from cavitating because it is measured just as cavitation begins to start. Therefore, the NPSHa should always be greater than NPSHr to keep a positive margin and prevent cavitation.

Steps to avoid pump cavitation 

The main focus should be to prevent unnecessary pressure drop. Additional pressure drop can often be avoided by removing as many valves and bends as possible and moving the pump closer to the fluid source. The distance between the fluid source and the pump should be decreased if the suction lift requirement is too high and would cause a pressure drop. 

Sometimes there are blockages in the piping or hoses near the pump so enlarging suction lines can mitigate the problem. The suction lines should also be cleaned regularly. In addition to these basic steps, there are a few other effective ways to curb cavitation. 

Pump selection

Cavitation is increased when the pump head drops so selecting the correct pump ensures a positive margin of the NPSHa above NPSHr. Keeping the pressure at the pump inlet 10% greater than the pump specific NPSHr is a good general rule to prevent cavitation. For an NPSHr of 10 feet, an 11 feet NPSHa is a good value. Contrary to NPSHr (which is a pump specific value and cannot be changed), the NPSHa is a system-specific value and can be increased by the following steps:

• Elevating the supply tank
• Raising and maintaining tank liquid level
• Cleaning debris inside the pipes
• Reducing piping losses caused by unnecessary valves and fittings

Preventing discharge cavitation

Discharge cavitation is observed when the pressure at the discharge end of the pump is very high. This limits the volume of the fluid exiting from the pump and high-velocity fluid remains trapped between the impeller and housing. This is a major cause of cavitation. Causes of high discharge pressure include pipe blockages, poor piping design, and clogged filters. 

To prevent discharge cavitation, reducers should be kept as close as possible to the pump. In addition, pockets should be avoided that allow air and vapor to accumulate. The control valves (if they are needed) should always be installed on the discharge side instead of the suction side of the pump.

Ensuring pump maintenance

Ensuring routine pump maintenance is a proven method to avoid cavitation. The maintenance activities can include:

• Cleaning blocked filters and strainers to avoid discharge pressure buildup. A maintenance schedule should be set up for regular cleaning. 

• Checking the pressure sensing equipment. 

• Ensuring that there are no cracks or collapsed points in the piping and hoses.

Installing the system properly

The system should be designed such that the NPSHa is greater than the NPSHr. There are four factors that have to be considered for an appropriate system design:

Pump location

The pump should be installed in such an orientation that the pump suction inlet lines have an adequate slope and the pump housing is flooded. It should be ensured that the fluid flows smoothly into the pump suction inlet. 

The pump should be placed at a level that is lower than the fluid level in the supply tank. This pump orientation involves the force of gravity to maintain the flooded section of the pump. This helps to curb cavitation.

Size of the suction pipe

The pump suction diameter should be chosen carefully. This helps to maintain laminar flow. It is best to avoid elbows, valves, reducers, and strainers in the final length of the pipe. 

In addition, the pump casing should not be made to support the weight of the piping. This can cause strain on the pump casing. The piping should be supported on supports and hangers. The suction side of the pump should be always kept larger in size than the pump inlet.

Suction lift

The suction lift is the vertical distance from the water source to the pump inlet. A high suction lift can increase turbulence, ramp up energy demands, and most importantly, decrease NPSHa. The pump should therefore always be installed below the water level in the supply tank.

Friction loss

Friction loss in the piping system results in pressure drop that can cause cavitation. Friction losses are affected by pipe length, diameter, and flow rate. Obstructions in flow velocity can cause pressure changes that can trigger cavitation. 

In conclusion, there are a number of factors that initiate cavitation. If any trouble is encountered, the following list of quick checks can help in troubleshooting:

• Checking whether the pump is installed high above the fluid source or not
• Checking whether the pump suction line is sloped properly or not
• Checking if there are unnecessary fittings on the suction pipe
• Checking if the pump is running too fast
• Checking if the suction pipe diameter is too small or the pipe is too long