Pumps and Turbines Study Notes for SSC JE & AE JE Exams

In a Hydroelectric plant as shown above:

• A Dam is established across a river or a channel for storing water. The reservoir is also called as Head race. 
• Pipes of large diameter called Penstock which carry water under pressure from the storage reservoir to the turbines. These pipes are generally made of reinforced concrete or steel.
• Turbines having several types of vanes or buckets or blades mounted on a wheel called a runner.
• Tail-race is a channel carrying water away from the turbine after the water has worked on the turbines. The water surface in the tail-race is also called as tail-race level.

Important Terms

• Gross Head (H_g ): Vertical height difference between headrace and tailrace.
• Net Head (H_net): The actual head available for work on the turbine is called the Net Head.
  H_net = H_g - h_L
   h_L being the total head loss during the transit of water from the headrace to tailrace, mainly the head loss due to friction and is given by:
  
  'f' is the coefficient of friction of penstock which depends on the type of material of penstock, 'L' is the total length of penstock, 'V' is the mean flow velocity of water in the penstock, 'D' is the diameter of penstock and g is the acceleration due to gravity.
  Thus: 

Types of Efficiencies:

Considering different types of output and input, the efficiencies can be classified as:

• Hydraulic Efficiency(η_h)
  • The ratio of the power developed by the runner of a turbine to the power supplied at the inlet of the turbine is known as Hydraulic efficiency.
  • If R.P. is the Runner Power and W.P. is the Water Power:
    
     
• Mechanical Efficiency(η_m)
  • The ratio of the power available at the shaft to the power developed by the runner of a turbine is called Mechanical Efficiency.
  • If S.P . is the Shaft Power:
    
• Overall Efficiency(η_o):
  • The ratio of the power available at the shaft to the power supplied at the inlet of a turbine is termed as overall efficiency.
    

• Volumetric Efficiency

Hydraulic Turbines 

The hydraulic machines which are used for the conversion of hydraulic energy into mechanical energy are known as Hydraulic Turbines.

Classification of Turbines

• The hydraulic turbines can be classified on the basis of type of energy at the inlet, the direction of flow through the vanes, head available at the inlet, discharge through the vanes and specific speed.
• They are classified as:

•  Pelton Turbine:

  • Pelton wheel turbine is an impulse turbine. In this type of turbine nozzle is connected at the exit of penstock which converts the available energy head into velocity head.
    
    Where:
    u= wheel velocity
    V= Jet velocity
    V_r= relative velocity
    V_w=whirl velocity
    φ=Angle by relative velocity at outlet and β= Guide blade angle at outlet
    u₁=u₂=u=2πN/60 where N= no. of rotation of wheel
• Tangential flow impulse turbine:Basic components:
  (1). Nozzle  (2). Runner and buckets  (3). Casing   (4). Breaking Jet
  
  Hydraulic efficiency is given by:
      
        
                 

Radial Flow Reaction Turbine:

• In this type of turbine the water strikes the runner, it has both kinetic energy head and pressure energy head. Due to KE head, impulse will generate, which is similar as in case of impulse turbine.
• Impulse: kinetic head
  Reaction: Pressure head
  
• Let B₁, B₂ = width of runner at inlet and outlet
  Area of flow at inlet: A₁ = πD₁B₁
  Area of flow at inlet: A₂ = πD₂B₂
  If vane thickness is taken into consideration:
  Net Area of flow = [πD₁ – nt] · B₁ = kπD₁B₁
  K is factor for net area and n is the number of vanes.
  

Francis turbine:

• Francis turbine is an inward flow reaction turbine.
• To maximize runner power, V₂ should be minimum. It can be done by converting absolute velocity direction into radial direction to the runner at exit.
  

Degree of Reaction (R):

          ............ (1)

Thus, degree of reaction of the Pelton turbine is zero.

(ii). For Francis turbine:

Axial flow Reaction turbine:

Propeller and Kaplan turbines are the example of axial flow reaction turbine.

Draft Tube: 

• A draft tube is a pipe of a gradually increasing cross sectional area, connecting the runner outlet to the tailrace and is used to discharge water from the turbine exit to the tail-race.
• An end of the draft tube is connected to the runner outlet and the other end is submerged under the level of water in the tail-race.

Functions:

• It allows a negative head to be established at the outlet of the runner and thereby increasing the NET HEAD on the turbine.
• It converts a large proportion of kinetic energy which was being rejected at the outlet if the turbine into useful pressure energy.
  
  Draft tube efficiency is given by: 
  

Specific Speed:

• The value of specific speed for a turbine is the speed of a geometrically similar turbine which would produce unit power (one kilowatt) under a unit head (one meter).
• This value is provided by the manufacturer (along with other ratings) and will always refer to the point of maximum efficiency.
   
• Specific Speed is not a dimensionless number. It's dimension [M^1/2L^-1/4T^-5/2].

Model Laws:

Hydraulic Pumps

The hydraulic machines which are used for the conversion of mechanical energy into hydraulic energy are known as Hydraulic Pumps.

Hydraulic Pumps are classified as 

Rotary pumps (Centrifugal pumps)

positive displacement pumps (Reciprocating pumps)

Centrifugal Pumps

• A hydraulic machine which converts mechanical energy into hydraulic energy or pressure energy is known as a pump.

Classification of Centrifugal Pumps:

Heads on a centrifugal pump:

• Suction head (h_s)
  • It is the vertical distance between the liquid level in the sump and the centre line of the pump.
  • It is expressed as meters.
• Delivery head (h_d)
  • It is the vertical distance between the centre line of the pump and the liquid level in the overhead tank or the supply point.
  • It is expressed in meters.
• Static head (Hs)
  • It is the vertical difference between the liquid levels In the overhead tank and the sump when the pump is not working.
  • It is expressed as meters.
    Therefore: H_s= (h_s+ h_d)

• Friction head (h_f)
  • It is the sum of the head loss due to the friction in the suction and delivery pipes.
  • The friction loss in both the pipes is calculated using the Darcy‟s equation.
     
• Total head (H)
  •  It is the sum of the static head H_s, friction head (h_f) and the velocity head in the delivery pipe (V²_d /2g). Where, V_d=velocity in the delivery pipe.
    

• Manometric head(H_m)
  • It is the total head developed by the pump.
  • This head is slightly less than the head generated by the impeller due to some losses in the pump.
    

• Power of pump:
  (i). Power requirement of pump = shaft power (SP)
  (ii). Impeller power (IP) = SP – (mechanical frictional losses)
  (iii). Manometric power or output power (MP)= ρQgH_m
  
  
• Efficiencies:
  (i). Manometric efficiency (η_m):
  
  (ii). Mechanical Efficiency:
  
  (iii). Overall efficiency: It is defined as ratio of power output of the pump to the power input to the pump. The power output of the pump in kW:
  
  (iv). Volumetric Efficiency:
  
• Specific speed  of pump:
  
  Non-dimensional form of specific speed ⇒ It is called the Shape number of pump.
  
• Model Testing of pumps:
  
  
  
  
• Priming of centrifugal Pump:
  Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe up to the delivery valve is completely filled up from outside source with the liquid to be raised by the pump before starting the pump.Thus, the air from these parts of the pump is removed and these parts are filled with the liquid to be pumped.
  Minimum starting speed of pump:
  
  
• Cavitation:
  (i). Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapour pressure and the sudden collapsing of these vapour bubbles in a region of higher pressure.
  (ii). Cavitation results in decrease in turbine efficiency, pitting action, noise and vibration.
• Net Positive Suction Head (NPSH): 
  (i). The net head developed at the suction port of the pump, in excess of the head due to the  vapor pressure of the liquid at the temperature in the pump.
  (ii). NPSH must be positive for preventing the liquid from boiling. Boiling or cavitation may damage the pump.
  
  where, P_v is the vapor–pressure of the liquid. If the pump is placed at a height 'z' above the free surface of a liquid where the atmosphere pressure is P.
• Multi Staging of Pumps:
  (i). Pumps in series:The series connection of the pumps is used to increase the total head delivered by the pump.
  Q = constant
  (ii). Pumps in Parallel:The parallel connection of the pumps is used to increase the total head delivered by the pump.
  H_m = constant
  Reciprocating pumps:
  In the reciprocating pumps the mechanical energy is converted to hydraulic energy (or pressure energy) by sucking the liquid into a cylinder in which a piston is reciprocating (moving backwards and forward) which exerts the thrust on the fluid and increases the pressure energy.
  Discharge (Q) is given by:
  (i).For Single acting pumps:
    
  (ii). For double acting pumps:
     
  Slip in Reciprocating pumps:
   
  Power in reciprocating pumps:
  

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