Power and Efficiency MCQ Quiz - Objective Question with Answer for Power and Efficiency - Download Free PDF

Explanation:

Two-Stroke Petrol Engine:

• A two-stroke petrol engine is a type of internal combustion engine that completes a power cycle in two strokes of the piston during only one crankshaft revolution. In this type of engine, the inlet port, transfer port, and exhaust port play crucial roles in ensuring the proper intake of the air-fuel mixture, transfer of the mixture to the combustion chamber, and expulsion of exhaust gases.
• The opening and closing of the inlet port in a two-stroke engine are controlled by the movement of the piston itself. Unlike in four-stroke engines, there are no valves in a traditional two-stroke engine; instead, ports are used. The timing of these ports is critical for the efficient operation of the engine.

30° to 40° before BDC:

• The inlet port begins to open when the piston is moving towards the bottom dead center (BDC), which allows the fresh air-fuel mixture to enter the crankcase. This occurs slightly before the piston reaches BDC, typically in the range of 30° to 40° before BDC, to ensure that the mixture has enough time to flow into the crankcase under the influence of the pressure difference created by the piston's motion.

Working Mechanism:

1. Induction Phase: As the piston moves downward during its power stroke, it simultaneously uncovers the inlet port. This movement creates a low-pressure area in the crankcase. The fresh air-fuel mixture is then drawn into the crankcase through the inlet port due to the pressure difference.

2. Timing of Inlet Port Opening: The inlet port opens slightly before the piston reaches BDC, as specified in the range of 30° to 40° before BDC. This ensures that the air-fuel mixture starts entering the crankcase at the optimal time, maximizing the engine's efficiency and power output.

3. Transfer and Exhaust Phases: Once the piston starts moving upward after reaching BDC, it compresses the air-fuel mixture in the crankcase. At the same time, the transfer port and exhaust port open to allow the fresh mixture to enter the combustion chamber and the exhaust gases to exit, respectively.

Solution:

Given that Diameter of the brake drum, $D=1.2\text{m}$ , Thickness of the brake lining, $d=12.5\text{mm}=0.0125\text{m}$ , Speed of rotation, $N=200\text{r.p.m}$

Load applied, $W=600\text{N}$

Spring force, $S=150\text{N}$

We know that the brake power (B.P.) of the engine is given by:

$B.P.=\frac{(W-S)\pi (D+d)N}{60}$

Substituting the given values:

$B.P.=\frac{(600-150)\pi (1.2+0.0125)200}{60}$

Simplifying:

$B.P.=5715\text{W}$ = 5.715 kW

Explanation:

Relative Efficiency:

• The relative efficiency of an engine is defined as the ratio of the actual brake thermal efficiency to the theoretical efficiency of the engine cycle.
• It is a measure of how closely an engine's performance approaches the ideal performance predicted by the thermodynamic cycle on which the engine is based.

Brake Thermal Efficiency:

• Brake thermal efficiency is the efficiency of an engine, defined as the ratio of the brake power output to the fuel energy input.
• It is a measure of how efficiently the engine converts the energy in the fuel to mechanical power output.

Combustion Efficiency:

• Combustion efficiency refers to how effectively an engine burns the fuel.
• It is the ratio of the actual heat released during combustion to the theoretical heat release if the fuel were to burn completely.

Scavenging Efficiency:

• Scavenging efficiency is specific to two-stroke engines and refers to the effectiveness of removing exhaust gases from the cylinder and replacing them with a fresh air-fuel mixture.

Additional Information

Other efficiencies related to engine performance include:

(1) Volumetric Efficiency:

• Volumetric efficiency is the ratio of the actual volume of air inducted by the engine to the theoretical volume it could induct at the same conditions.

(2) Mechanical Efficiency:

• Mechanical efficiency is the ratio of the brake power output to the indicated power output of the engine.

(3) Thermal Efficiency:

• Thermal efficiency is the ratio of the engine's output work to the heat input from the fuel.

Explanation:

Rope brake dynamometer:

• A rope brake dynamometer is a type of device used to measure the mechanical power output of an engine or a motor.
• It is often employed in laboratories and testing facilities to assess the performance characteristics of engines, particularly in terms of their power output and efficiency.
• It is another form of absorption type dynamometer which is most commonly used for measuring the brake power of the engine.
• It consists of one, two or more ropes wound around the flywheel or rim of a pulley fixed rigidly to the shaft of an engine.
• The upper end of the ropes is attached to a spring balance while the lower end of the ropes is kept in position by applying a dead weight as shown in Figure.
• In order to prevent the slipping of the rope over the flywheel, wooden blocks are placed at intervals around the circumference of the flywheel.
• In the operation of the brake, the engine is made to run at a constant speed.
• The frictional torque, due to the rope, must be equal to the torque being transmitted by the engine.

Formula for Brake Power:

The brake power of an engine using a rope brake dynamometer can be calculated using the following formula:

BP = (π × D × N × (W - S)) / 60

Where:

• D = Diameter of the brake drum (in meters)
• N = Speed of the engine in revolutions per minute (rpm)
• W = Weight (in Newtons)
• S = Spring scale reading (in Newtons)

Volumetric efficiency is defined as the ratio of an actual volume flow rate of air into the system to the rate at which the volume is displaced by the system.

Volumetric efficiency:

• It is a measure of the engine breathing capacity - varies from low (during low speeds) to a peak at about 2/3rd of the speed range and again to a low value at higher speeds.
• The reason for this is the engine piston speed and valve timing.
• At low speeds, the valves stay open for a longer time but the suction in the engine is less because the piston moves slowly. Because of this, the air intake into the engine is lesser than what is maximum possible.
• As the engine picks up speed, the higher piston speed creates more suction which makes the engine intake more and more air with each stroke. This increases the volumetric efficiency which peaks at a speed for a given engine and thus increasing the Torque.
• Beyond this speed, flow losses at the intake valve dominate due to the increase in air intake velocity and this causes lesser and lesser air to be taken in per stroke. This reduces the Volumetric efficiency.

Concept:

Mechanical efficiency at half load $=\frac{BP}{BP+FP}$

Calculation:

Given: 

Brake power (BP) = 200 kW, Half load = 100 kW Friction Power (FP) = 25 kW

Mechanical efficiency at half load $=\frac{BP}{BP+FP}$

Mechanical efficiency at half load $=\frac{100}{125}$

Mechanical efficiency at half load = 0.8 ⇒ 80 %

Concept:

A dynamometer is a device used for measuring the torque and brake power required to operate a driven machine. It has a device to measure the frictional resistance.

The following are the two types of dynamometers, used for measuring the brake power of an engine.

• Absorption dynamometers: The entire energy or power produced by the dynamometer is absorbed by the friction resistance of the brake and is transformed into heat, during the process of measurement.
  • Example: Prony brake dynamometer, Rope brake dynamometer, Hydraulic dynamometer, Eddy current dynamometer.
• Transmission dynamometers: The energy is not wasted in friction but is used for doing work. The energy or power produced by the engine is transmitted through the dynamometer to some other machines where the power developed is suitably measured.
  • Examples: Epicyclic-train dynamometer, Belt transmission dynamometer, Torsion dynamometer.

Concept:

Mechanical efficiency:

${\eta }_m=\frac{BrakePower}{IndicatedPower}=\frac{B.P.}{I.P.}$

Indicated thermal efficiency:

${\eta }_{ith}=\frac{IndicatedPower}{Heataddedpersecond}$

Heat added per second HA/s =  ${\dot{m}}_f\times$ (C.V.)_f, where C.V. = Calorific value of fuel 

Calculation:

Given:

Brake power, B.P = 4.5 kW, Indicated thermal efficiency η_ith = 30% = 0.3, Mechanical efficiency η_m = 85%, Calorific value (C.V)_f = 40000 kJ/kg

${\eta }_m=\frac{B.P}{I.P.}$  ⇒  $I.P=\frac{B.P}{{\eta }_m}=\frac{4.5}{0.85}$ = 5.294 kW

${\eta }_{ith}=\frac{I.P}{HA/s}$

$HA/s=\frac{I.P}{{\eta }_{ith}}=\frac{5.294}{0.3}=17.647kW$ 

where I.P = indicated power, HA/s = Heat added per second

$HA/s={\dot{m}}_f\times {C.V}_f$ = 17.647 kJ/s

${\dot{m}}_f=\frac{17.647\times 3600}{40000}$ = 1.6 kg/hr.

Concept:

Brake thermal efficiency$\left({\eta }_{bth}\right)=\frac{BP}{m_f\times CV}$

where, BP = Brake power of IC engine, m_f = fuel consumption, CV = Calorific value of the fuel

Calculation:

Given:

ηbth = 0.3, CV = 40 × 10³ kJ/kg, BP = 15 kJ/s

Now,  

∴ $0.3=\frac{15}{40\times {10}^3\times m_f}$

$m_f=\frac{15}{0.3}\times \frac{1}{40000}\times 3600\frac{kg}{hr}$

∴ mf = 4.5 kg/hr

Explanation:

Volumetric efficiency of an engine

• Volumetric efficiency is a measure of the success with which the air supply and thus the charge is inducted into the engine
• It is a very important parameter since it indicates the breathing capacity of the engine.
• Volumetric efficiency is defined as the ratio of mass of air actually drawn into the cylinder to the mass of air that ideally could be drawn into cylinder.
• ${\eta }_v=\frac{m_{air}^{.}\left(measured\right)}{{\rho }_{air}{V}_d\times \frac{N}{n}}$ where V_d = volume of the cylinder, N = rotation per sec, n = no. of rotation per cycle
• For 4-stroke engine, n = 2 and for 2-stroke engine, n = 1

Important Points

• The volumetric efficiency of a SI engine is generally lies in the range of 71% - 90%.
• The volumetric efficiency of a CI engine is generally lie in the range of 85 – 90%

Concept:

Indicated Power is the power developed inside the cylinder of the engine.

I.P = P_mean × V_s kW or $IP=\frac{P_{m}LAN}{60\times 1000}kW$

Calculation:

Given:

L = 120 mm, D = 80 mm, P_m = 4 × 10⁵ N/m², N = 1500 rpm

Indicated Power:

$IP=\frac{4\times {10}^5\times 120\times \frac{\pi }{4}{\left(80\right)}^2\times {10}^{-9}\times 1500}{60\times 1000}=6.03kW$

Concept:

Morse Test for Mechanical Efficiency Calculation

In a Morse test on a 2-cylinder, 2-stroke SI engine, the brake power (BP) is 9 kW and the BHP of individual cylinders with spark cut-off are 4.25 kW and 3.75 kW, respectively. The mechanical efficiency of the engine is calculated as follows:

Step-by-Step Solution:

1. Calculate the Indicated Power (IP):

- The Indicated Power for each cylinder can be determined when its spark is cut off.

- For the first cylinder: IP₁ = Total BP - BP with first cylinder cut-off = 9 kW - 4.25 kW = 4.75 kW

- For the second cylinder: IP₂ = Total BP - BP with second cylinder cut-off = 9 kW - 3.75 kW = 5.25 kW

- Total Indicated Power (IP) is: IP = IP₁ + IP₂ = 4.75 kW + 5.25 kW = 10 kW

2. Calculate the Mechanical Efficiency (η_m):

- Mechanical efficiency is the ratio of Brake Power (BP) to Indicated Power (IP):

- η_m = (BP / IP) × 100 = (9 kW / 10 kW) × 100 = 90%

Therefore, the mechanical efficiency of the engine is 90%.

Answer: 1) 90%

Concept:

Break power: $bp=\frac{\pi DN\left(W-S\right)}{60}watt$

Where D = effective brake drum diameter

N = rpm

W = dead weight

S = spring balance reading

Calculation:

Given, D = 600 + 26 = 626 mm

N = 450 rpm

W = 200 N

S = 30 N

$\therefore bp=\frac{3.14\times 0.626\times 450\times \left(200-30\right)}{60,000}$

Concept:

The work input to the piston is due to the expansion of hot gases. Thus the work input to the piston is found by the pressure and volume changes in the p-v diagram, known as the indicator diagram. Thus the work input to the piston is known as indicator work done (IWD).

The work output from the piston is found by a brake mechanism attached to the shaft of the engine, this mechanism is known as a dynamometer. Hence the work output of the piston is known as brake work done (BWD).

The ratio of brake work done to indicated work done is known as mechanical efficiency.

${\eta }_m=\frac{BWD}{IWD}=\frac{b_{mep}\times V_s}{i_{mep}\times V_s}=\frac{brakepower\left(BP\right)}{indicatedpower\left(IP\right)}$

where   

b_mep = Break mean effective pressure,

i_mep = Indicated mean effective pressure,

V_s = Stroke volume                                         

IP = BP + FP

FP = Frictional Power

Calculation:

Given:

Mechanical efficiency η_m = 90 %

Frictional power, FP = 30 kW

IP = BP + FP

$\frac{BP}{0.9}=BP+30$

∴ BP = 270 kW.

Explanation:

A dynamometer is a device used for measuring the torque and brake power required to operate a driven machine. It has a device to measure the frictional resistance. 

Following are the two types of dynamometers, used for measuring the brake power of an engine.

• Absorption dynamometers: The entire energy or power produced by the engine is absorbed by the friction resistances of the brake and is transformed into heat, during the process of measurement.
• Example: Prony brake dynamometer, Rope brake dynamometer, Hydraulic dynamometer 
• Transmission dynamometers: The energy is not wasted in friction but is used for doing work. The energy or power produced by the engine is transmitted through the dynamometer to some other machines where the power developed is suitably measured.
• Examples: Epicyclic-train dynamometer,  Belt transmission dynamometer, and Torsion dynamometer.