Turbomachinery MCQ Quiz - Objective Question with Answer for Turbomachinery - Download Free PDF

Concept:

The pitch diameter of a Pelton wheel is calculated by equating the tangential velocity derived from geometry and speed ratio. The tangential velocity is:

and also

Equating both:

Final Answer:

Explanation:

Theoretical Power Required to Drive a Single-Acting Reciprocating Pump:

• The theoretical power required to drive a single-acting reciprocating pump is derived based on the fundamental principles of fluid mechanics and pump operation. The power required is a function of the work done by the pump in lifting the liquid through the given head, considering the weight of the liquid, the stroke volume, and the number of strokes per minute.

The theoretical power for a single-acting reciprocating pump is calculated by multiplying the volume of fluid delivered per second by the specific weight and total head (suction + delivery).

\( P = \frac{w \times A \times L \times N}{60} (H_s + H_d) \)

Where:

• \( w \): Specific weight of the fluid
• \( A \): Cross-sectional area of the piston
• \( L \): Length of stroke
• \( N \): Number of delivery strokes per minute
• \( H_s \): Suction head
• \( H_d \): Delivery head

Concept:

The overall efficiency of a Francis turbine is defined as the ratio of useful power output at the runner shaft to the hydraulic power input from water striking the runner.

Formula:

Hydraulic Power Input = Weight of water per second × Net Head

\( \lambda_0 = \frac{\text{Power Output}}{\text{Hydraulic Power}} = \frac{P}{W \cdot H} \)

Concept:

• The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which would deliver one cubic metre of liquid per second against a head of one metre.
• \({N_s} = \frac{{N\sqrt Q }}{{H_m^{3/4}}}\)

Important Points

• The specific speed (Ns) of a turbine is defined as, the speed of a geometrically similar Turbine that would develop unit Power (P) when working under a unit Head (H) (1 m head).
• Specific speed for the turbine is given by:
• \({N_s} = \frac{{N\sqrt P }}{{{H^{\frac{5}{4}}}}}\)
•  

Explanation:

• Hydroelectric power plants serve multiple purposes beyond electricity generation, such as irrigation, flood control, water supply, and recreation.

• They store water in large reservoirs, which can be regulated to meet seasonal and agricultural demands.

• During heavy rains, controlled release of water helps prevent downstream flooding.

• Stored water can be supplied to nearby towns or industries as a dependable water source.

• Reservoirs created by dams are often used for tourism, boating, and fishery development.

 Additional Information

• Hydroelectric power uses the potential energy of stored water at a height, converting it to mechanical energy through turbines and then to electrical energy via generators.

• These plants are built on rivers with dams, which create large reservoirs to control water flow and ensure consistent power generation throughout the year.

• They are considered renewable energy sources, as water is naturally replenished by the hydrological cycle without emitting pollutants.

• Hydroelectric plants have low operating and maintenance costs once installed and can respond quickly to demand fluctuations due to their flexible operations.

• These plants also contribute to grid stability and peak load supply, especially when paired with other sources of energy.

Explanation:

Positive displacement pump:

• Positive displacement pumps are those pumps in which the liquid is sucked and then it is pushed or displaced to the thrust exerted on it by a moving member, which results in lifting the liquid to the required height.
• Reciprocating pump, Vane pump, Lobe pump are the examples of positive displacement pump whereas the centrifugal pump is the non-positive displacement pump.​

Concept:

Pelton wheel:

It is a tangential flow impulse turbine in which the pressure energy of water is converted into kinetic energy to form a high-speed water jet and this jet strikes the wheel tangentially to make it rotate.

Taygun's formula:

It is used to determine the number of buckets on the runner in the Pelton wheel turbine. It is given by the below formula:

\(Z = 15+{ D\over 2d}\)

Where D = Pitch or mean diameter, d = Nozzle or Jet  diameter

Calculation:

Given,

D = 1 m, d = 0.1 m

The number of buckets on the runner by Taygun's formula

\(Z = 15+{ D\over 2d} = 15+{ 1\over 2\times 0.1}\)= 15 + 5 = 20

Concept:

The overall efficiency η_o of turbine = volumetric efficiency (η_v)× hydraulic efficiency (η_h)× mechanical efficiency (η_m)

\({\eta _o} = {\eta _v} \times {\eta _h} \times {\eta _m}\)

\({{\rm{\eta }}_{\rm{v}}} = \frac{{{\rm{volume\;of\;water\;actually\;striking\;the\;runner}}}}{{{\rm{volume\;of\;water\;actually\;supplied\;to\;the\;turbine}}}}\)

\({{\rm{\eta }}_{\rm{h}}} = \frac{{{\rm{Power\;deliverd\;to\;runner}}}}{{{\rm{Power\;supplied\;at\;inlet\;}}}} = \frac{{{\rm{R}}.{\rm{P}}}}{{{\rm{W}}.{\rm{P}}}}\)

\({{\rm{\eta }}_{\rm{m}}} = \frac{{{\rm{Power\;at\;the\;shaft\;of\;the\;turbine}}}}{{{\rm{Power\;delivered\;by\;water\;to\;the\;runner}}}} = \frac{{{\rm{S}}.{\rm{P}}}}{{{\rm{R}}.{\rm{P}}}}\)

Overall efficiency: \({\eta _o} = \frac{{S.P}}{{W.P}}\)

Water Power = ρ × Q × g × h 

Calculation:

Given:

η_o = 0.8, Head h = 10 m, and Q = 1 m³/s.

\({\eta _o} = \frac{{S.P}}{{W.P}} = \frac{{S.P}}{{\rho \times Q \times g \times h}}\)

\(0.8 = \frac{{S.P}}{{1000 \times 1 \times 9.81 \times 10}} \Rightarrow S.P = 78480\;W \approx 78\;kW\)

Explanation:

Flow ratio

The flow ratio of Francis turbine is defined as the ratio of the velocity of flow at the inlet to the theoretical jet velocity.

\(Flow\;Ratio = \frac{{{V_{f1}}}}{{\sqrt {2gH} }}\)

In the case of Francis turbine,

Flow ratio varies from 0.15 to 0.3

Speed ratio varies from 0.6 to 0.9

Calculation:

\(Flow\;Ratio = \frac{{7}}{{\sqrt {2\times10\times62} }}=0.2\)

Explanation:

Draft tube

It is a conduit which connects the runner exit to the tailrace where the water is being finally discharged from the turbine.

Hence, Draft tube at the exit of a reaction turbine used for the hydroelectric project is always immersed in water.

Function

Pump: 

The hydraulic machine that converts mechanical energy into hydraulic energy is called a pump

Nozzle: 

It is a pipe or tube of varying cross-sections. It is generally used to control the pressure or rate of flow.

Turbine: 

The main function of prime movers or hydro turbines is to convert the kinetic energy of the water into mechanical energy to produce electric power.

Boiler: 

It is a closed vessel in which steam is produced from water by the combustion of fuel.

Explanation:

Specific speed:

• It is defined as the speed of a geometrically similar pump that would deliver one cubic meter of liquid per second against the head of one meter.
• It is used to compare the performances of 2 different pumps.
• Its dimension is M⁰L^3/4T^-3/2 and given by the formula and is given by
   

\(N_{s}=\frac{N\sqrt{Q}}{H_{m}^{3/4}}\)

Where N_S = Specific speed, Q = Discharge, H = Head under which the pump is working, N = Speed at the pump is working.

Additional Information

(specific speed for turbines) = \({{\rm{N}}_{\rm{s}}} = \frac{{{\rm{N}}{\sqrt{P}}}}{{{{\rm{H_m}}^{5/4}}}}\)

Non-dimensional specific speed is given by

\({N_S} = \frac{{N\sqrt P }}{{{{\left( {gH} \right)}^{\frac{5}{4}}} \cdot \sqrt \rho }}\)

The Francis turbine is a type of reaction turbine, and it can operate over a wide range of water flows and height differences, which makes it suitable for a specific speed value of 1. It is more flexible in terms of operation conditions compared to the Pelton wheel.

Explanation:

Overall Efficiency (η): It is defined as a ratio of the power output of the pump to the power input to the pump.

The overall efficiency of the pump will be given as,

\({{\rm{\eta }}_{\rm{}}} = \frac{{{\rm{water\;power}}}}{{{\rm{shaft\;power\;}}}} = \frac{{{\rm{\omega QH}}}}{{\rm{P}}}\)

\(P = \frac{{{\bf{\omega QH}}\;}}{{{\eta }}}\)

Calculation:

\(\eta = \frac{{{\bf{\rho g QH}}\;}}{{{P }}} = \frac{{{\bf{1000\times10\times0.04\times25}}\;}}{{{16000}}}=0.625\)

Additional Information

Manometric Efficiency (ηman): It is the ratio of the manometric head to head imparted by the impeller to the water.

\({\eta _{man}} = \frac{{{H_m}}}{{\frac{{{V_{w2}}{u_2}}}{g}}} = \frac{{g{H_m}}}{{{V_{w2}}{u_2}}}\)

Mechanical Efficiency (ηm): It is the ratio of the power available at the impeller to the power at the shaft of the centrifugal pump.

\({\eta _m} = \frac{{{\rm{Power\;at\;the\;impeller}}}}{{{\rm{Power\;at\;the\;shaft}}}} = \frac{{\frac{W}{g}\left( {\frac{{{V_{w2}}{u_2}}}{{1000}}} \right)}}{{{\rm{SP}}}}\)

Explanation:

Runoff river plants:

• A runoff river plant is defined as a plant that utilized minimum flow in a river and has no appreciable pondage on its upstream side. The excess water is temporarily stored in the pond on the upstream side when the discharge at the site is more than the demand.

Additional Information

Tidal plant:

• A tidal power plant is a plant that produces electricity using a source of renewable energy tides.

Pumped storage plant:

• A pump storage plant is a hydroelectric system in which electricity is generated during periods of high demand by the use of water that has been pumped into a reservoir.

Storage plant:

• A storage plant is defined as a plant used for the storage of energy in the form of water.