Hydraulic Pumps is an important topic in the subject of Fluid Mechanics and Machinary. In this article, we will list down important points to remember for the topic on hydraulic pumps from the point of view of GATE and UPSC ESE exams.

Hydraulic Pumps: It is a word which has been derived using water as the working fluid, but other liquids can also be used. The two most common kind of hydraulic pumps are:

  1. Centrifugal pumps
  2. Axial flow pumps

Centrifugal Pumps: This kind of pump is used to raise liquids from a lower to a higher level by creating the required pressure with the help of centrifugal action. The three important parts of centrifugal pumps are:

  1. impeller
  2. volute casing
  3. diffuser

Impeller: These are backward curved blades mounted on a wheel, which is mounted on the drive shaft of centrifugal pump. 

  • As the impeller rotates, the fluid that is drawn into the blade passages at the impeller eye and is accelerated as it is forced radially outwards.
  • The fluid has a very high velocity at the outer radius of the impeller.
  • To recover kinetic energy by changing it into pressure energy, diffuser blades may be used.
  • The fluid moves from the diffuser blades into the volute casing.
  • The functions of a volute casing is that it collects water and conveys it to the pump outlet. 

For best efficiency of the pump, it is assumed that water enters the impeller radially, i.e.  and .

Use Euler's pump equation:

The work done per second on the water per unit mass of fluid flowing is:  , where  

 = component of absolute velocity in the tangential direction

E = W/m = Euler's head and represents the ideal or theoretical head developed by the impeller only.

The flow rate is given by the expression: , where

 = radial component of absolute velocity and is perpendicular to the tangent at the inlet and outlet and 

b = width of the blade

The work done on the water by the pump consists of the following three parts:

  1.  = represents the change in kinetic energy of the liquid
  2.  = represents the effect of the centrifugal head or energy produced by the impeller
  3.  = represents the change in static pressure of the liquid, if the losses in the impeller are neglected

Slip Factor:

  • There is usually a slight slippage of the fluid with respect to the blade rotation. 

 

Slip factor, 

  • For purely radial blades, which are often used in centrifugal compressors, . Then, the slip factor becomes, , where n = number of vanes = (impeller tip diameter)/(eye tip diameter)
  • The Stanitz slip factor is given be, 
  • When applying slip factor, the Euler pump equation becomes, 
  • Slip: In centrifugal pumps and compressors, due to relative rotation of fluid in a direction opposite to that of impeller with the same angular velocity as that of an impeller. 

 

 

The figure below shows that the leading side of a blade, where there is a high pressure region while on the trailing side of the blade there is a low pressure region.

LP = low pressure region,

HP = high pressure region

  • Due to the lower pressure on the trailing face, there will be a higher velocity and a velocity gradient across the passage.
  • There is low velocity on the high pressure side and high velocity on the low pressure side
  • Velocity distribution is not uniform at any radius.

Losses in centrifugal pump operation:

The following are the various losses occuring the operation of a centrifugal pump. 

  1. Eddy losses at entrance and exit of the impeller
  2. Friction losses in the impeller
  3. Frictional and eddy losses in the diffuser, if provided
  4. Hydraulic losses in suction and delivery pipe
  5. Mechanical losses due to friction of the main bearings and stuffing boxes

A number of efficiencies are associated with these losses,

  1. Overall efficiency  = , where  = density of the fluid, Q = flow rate, H = total head developed by the pump,  = shaft power input. The term  is called fluid power developed by the pump.
  2. Casing efficiency  = Fluid power at casing outlet / Fluid power at casing inlet = Fluid power at casing outlet / (fluid power developed by impeller - leakage losses).
  3. Impeller efficiency  = Fluid power at impeller exit / Fluid power supplied to impeller = Fluid power at impeller exit / (Fluid power developed by impeller + impeller loss)
  4. Volumetric efficiency  = Flow rate through pump / Flow rate through impeller = Q / (Q+q)
  5. Mechanical efficiency  = Fluid power supplied to the impeller / Power input by the shaft = 
  6. The overall efficiency can be calculated as, 
  7. Hydraulic efficiency  = Actual head developed by the pump / Theoretical head developed by impeller = . H = manometric head.

The effect of impeller blade shape on performance:

The blade shapes can be classified as:

  1. Backward curved blades 
  2. Radial blades 
  3. Forward curved blades 

In the above figure,  is much reduced, and thus, such rotors have a low energy transfer for a given impeller tip speed. 

In the above blade configuration figure:

  • Enegrgy transfer value is high
  • As per the velocity diagram, the value of  is very high
  • High kinetic energy is seldom required, and its reduction to static pressure by diffusion in a fixed casing is difficult to perform in a reasonable sized casing.

In the above blade configuration:

  • Advantages for very high speed compressors requiring highest possible pressure
  • Relatively easier to manuacture
  • No complext bending stresses

Vaneless diffuser:

It consists simply of an annular passage without vanes surrounding the impeller. The size of the diffuser can be determined by using the continuity equation.

The mass flow rate at any radius can be found out by: . Where b = width of the diffuser passage and 

  • For frictionless flow in the diffuser, angular momentum is constant and
  • The tangential velocity component is usually very much larger than the radial velocity component, so the ratio of the inlet to oulet diffuser velocities are:
  • The above ration means that for a large reduction in the outlet kinetic energy, a diffuser with a large radius is needed.

In the next article, we will talk about Cavitation in Hydraulic pumps and Pump Selection. Feel free to leave comments and queries below in the comment section.