Scaling Laws for Fans, Pumps and Compressors
Pumps
Learning Objectives:
- Classify different types of pumps.
- Identify the components of a centrifugal pump.
- Analyze series and parallel pumping applications.
- Calculate the specific speed of a pump.
The two main forms are positive displacement type and centrifugal pumps.
In positive displacement type, the volume of liquid delivered is directly related to the displacement of the piston and therefore increases directly with speed and is not appreciably influenced by the pressure.
e.g. reciprocating piston pump and the rotary gear pump
The centrifugal type depends on giving the liquid a high kinetic energy which is then converted as efficiently as possible into pressure energy.
Centrifugal pump converts the mechanical energy into pressure energy by means of centrifugal force acting on fluid, which rises water or liquid from a lower level to higher level. The main components of a centrifugal pump are:
- Impeller
- Casing
- Suction pipe with a foot valve and a strainer
- Delivery pipe
Centrifugal Pumps in Series:
The Centrifugal pumps are employed in series to overcome a larger system head loss than one pump can reimburse for separately. When two similar centrifugal pumps operating at the similar speed with same volumetric flow rate contribute the similar pump head. As the inlet to the second pump is the outlet of the first pump, the head generated by both pumps is the total of the separate heads. The volumetric flow rate from the inlet of the primary pump to the outlet of the second stays the same.
\[Q_1 = Q_2\] \[H_{total} = H_1 + H_2\]
Centrifugal Pumps in Parallel:
As the inlet and the outlet of each pump are at similar points in the system, each pump must generate the same pump head. The sum flow rate in the system, though, is the sum of the separate flow rates for each pump. Whenever the system characteristic curve is consider with the curve for pumps in parallel, operating point at the intersection of the two curves symbolizes a higher volumetric flow rate than for a single pump and a greater system head loss. A greater system head loss takes place with the raised fluid velocity resultant from the raised volumetric flow rate. Since of the greater system head, the volumetric flow rate is really less than twice the flow rate attained by using a single pump. \[Q_{\mathrm{total}} = Q_1 + Q_2\] \[H_1 = H_2\]Mechanical efficiency:
The power at the shaft of the centrifugal pump is more than the power available at the impeller of the pump. The ratio of the power available at the impeller to the power at the shaft of the centrifugal pump is known as mechanical efficiency.
\[\eta =\dfrac{\mathrm{Power\ at\ the\ impeller}}{\mathrm{Power\ at\ the\ shaft}}\]

External gear pump
+- at Japanese Wikipedia., CC BY-SA 3.0, via Wikimedia Commons
Centrifugal pump attached to a motor
MokeryJ. Vectorized by Magasjukur2, CC BY-SA 3.0, via Wikimedia Commons

See page for author, CC0, via Wikimedia Commons
Efficiency of a Centrifugal Pump
Learning Objectives:
- Understand energy use of a pump and thereby calculate pump efficiency.
Mechanical efficiency:
The power at the shaft of the centrifugal pump is more than the power available at the impeller of the pump. The ratio of the power available at the impeller to the power at the shaft of the centrifugal pump is known as mechanical efficiency.
\[\large \eta =\frac{\mathrm{Power\ at\ the\ impeller}}{\mathrm{Power\ at\ the\ shaft}}\]
NPSH and Cavitation
Learning Objectives:
- Define cavitation and net positive suction head.
- Understand the concept and importance of Net Positive Suction Head for pump performance.
- Design a pipe/pump system that minimizes the risk of cavitation.
- Highlight the importance of preventing cavitation in pumps.
NPSH:
NPSH - Net Positive Suction Head is a term describing conditions related to cavitation, which is undesired and harmful.
Cavitation is the creation of vapor bubbles in areas where the pressure locally drops to the fluid vapor pressure. The extent of cavitation depends on how low the pressure is in the pump. Cavitation generally lowers the head and causes noise and vibration. Cavitation first occurs at the point in the pump where the pressure is lowest, which is most often at the blade edge at the impeller inlet.
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.
The margin of pressure over vapor pressure, at the pump suction nozzle, is Net Positive Suction Head (NPSH). NPSH is the difference between suction pressure (stagnation) and vapor pressure. In equation form: \[\mathrm{NPSH} = P_s - P_{vap}\]
Cavitation:
Cavitation is the formation of gas bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapor pressure. Bubbles form at low pressures when the absolute pressure drops to the vapour pressure and the liquid spontaneously boils. (Bubbles may also arise from dissolved gases coming out of solution.)When the bubbles are swept into higher-pressure regions they collapse very rapidly, with large radial velocities and enormous short-term pressures. The problem is particularly acute at solid surfaces.
Cavitation may cause performance loss, vibration, noise, surface pitting and, occasionally,major structural damage. Besides the inlet to pumps the phenomenon is prevalent in marine-current turbines,ship and submarine propellers and on reservoir spillways.

Air Accidents Investigation Branch, Department for Transport, UK, OGL 3, via Wikimedia Commons
Turbines
Learning Objectives:
- Understand types of turbines as Impulse and reaction turbine and understand the difference in their working principle.
- Discuss working of common turbines: Pelton wheel, Francis and Kaplan turbine.
- Understand necessity of compounding in turbines.
A hydraulic turbine uses potential energy and kinetic energy of water and converts it into usable mechanical energy. The mechanical energy made available at the turbine shaft is used to run an electric power generator which is directly coupled to the turbine shaft. In a turbine, blades or buckets are provided on a wheel and directed against water to alter the momentum of water. As the momentum is changed with the water passing through the wheel, the resulting force turns the shaft of the wheel performing work and generating power.
Impulse Turbine:
In the impulse turbine, the total head of the incoming fluid is converted in to a large velocity head at the exit of the supply nozzle. That is the entire available energy of the water is converted in to kinetic energy. Although there are various types of impulse turbine designs, perhaps the easiest to understand is the Pelton wheel turbine. It is most efficient when operated with a large head and lower flow rate.
Jahobr, CC0, via Wikimedia Commons
Reaction Turbine:
Reaction turbines on the other hand, are best suited -for higher flow rate and lower head situations. In this type of turbines, the rotation of runner or rotor (rotating part of the turbine) is partly due to impulse action and partly due to change in pressure over the runner blades; therefore, it is called as reaction turbine. For, a reaction turbine, the penstock pipe feeds water to a row of fixed blades through casing. These fixed blades convert a part of the pressure energy into kinetic energy before water enters the runner. The water entering the runner of a reaction turbine has both pressure energy and kinetic energy. Water leaving the turbine is still left with some energy (pressure energy and kinetic energy). Since, the flow from the inlet to tail race is under pressure, casing is absolutely necessary to enclose the turbine. In general, Reaction turbines are medium to low-head, and high-flow rate devices. The reaction turbines in use are Francis turbine and Kaplan turbine.
Jahobr, CC0, via Wikimedia Commons
Axial Flow Turbines:
If the water flows parallel to the axis of the rotation of the shaft, the turbine is known as axial flow turbine. If the head at the inlet of the turbine is the sum of pressure energy and kinetic energy and during the flow of water through runner a part of pressure energy is converted into kinetic energy, the turbine is known as reaction turbine.
For the axial flow reaction turbines, the shaft of the turbine is vertical. The lower end of the shaft is made larger which is known as hub. The vanes are fixed on the hub and hence hub acts as runner for axial flow reaction turbine.
The important type of axial flow turbines are Propeller turbine and Kaplan turbine.
- When the vanes are fixed to the hub and they are not adjustable, the turbine is known as propeller turbine.
- If vanes on hub are adjustable the turbine is known as a Kaplan turbine. This turbine is suitable where a large quantity of water at low heads is available.
Radial Flow Turbines:
Radial flow turbines are those turbines in which the water flows in radial direction. The water may flow radially from outwards to inwards or from inwards to outwards.
If the water flows from outwards to inwards through the runner, the turbine is known as inward radial flow turbine. If the water flows from inwards to outwards, the turbine is known as outward radial flow turbine.
Reaction turbine means that the water at inlet of turbine possesses kinetic energy as well as pressure energy.
The main parts of a radial flow reaction turbine are:
- Casing: The water from penstocks enters the casing which is of spiral shape in which area of cross section of casing goes on decreasing gradually. The casing completely surrounds the runner of the turbine.
- Guide mechanism: It consists of stationary circular wheel all round the runner of the turbine. The stationary guide vanes are fixed on guide mechanism. The guide vanes allow the water to strike the vanes fixed on the runner without shock at inlet.
- Runner: It is a circular wheel on which a series of radial curved vanes are fixed. The surfaces of the vanes are made very smooth. The radial curved are so shaped that the water enters and leaves without shock.
- Draft tube: The pressure at the exit of the runner of reaction turbine is generally less than atmospheric pressure. The water exit cannot be directly discharged to the tail race.
A tube or pipe of gradually increasing area is used for discharging water from the exit of turbine to the tailrace. This tube of increasing area is called draft tube.
Solved Example: 345345
A Francis turbine is primarily used in:
A. High head applications
B. Low head applications
C. Wind applications
D. Thermal power plants
Correct Answer: A
Solved Example: 3465346
Which component is essential for the operation of a gas turbine?
A. Nozzle
B. Boiler
C. Cooling system
D. Pump
Correct Answer: A
Solved Example: 456456
What is the primary function of a turbine?
A. To convert thermal energy into mechanical energy
B. To convert mechanical energy into electrical energy
C. To convert kinetic energy into thermal energy
D. To convert potential energy into kinetic energy
Correct Answer: B
Solved Example: 4567567
What is the main advantage of using a gas turbine over a steam turbine?
A. Higher efficiency
B. Lower emissions
C. Smaller size
D. All of the above
Correct Answer: D
Solved Example: 546457
The primary use of a Kaplan turbine is in:
A. Wind energy
B. High head hydroelectric plants
C. Low head hydroelectric plants
D. Thermal power plants
Correct Answer: C
Solved Example: 567567
In a steam turbine, the steam expands and:
A. Increases in pressure
B. Loses heat
C. Increases in temperature
D. Increases in velocity
Correct Answer: D