A multicylinder gasoline engine in an airplane, operating at...

A multicylinder gasoline engine in an airplane, operating at 2500 rev/min, takes in energy $7.89 \times 10^{3} \mathrm{J}$ and exhausts $4.58 \times 10^{3} \mathrm{J}$ for each revolution of the crankshaft. (a) How many liters of fuel does it consume in 1.00 $\mathrm{h}$ of operation if the heat of combustion is $4.03 \times 10^{7} \mathrm{J} / \mathrm{L}$ ? (b) What is the mechanical power output of the engine? Ignore friction and express the answer in horsepower. (c) What is the torque exerted by the crankshaft on the load? (d) What power must the exhaust and cooling system transfer out of the engine?

Key Concepts

Energy Balance in Engines

This concept involves accounting for all the energy entering and leaving an engine system. In internal combustion engines, chemical energy from the fuel is converted into thermal energy and then to mechanical work, with a portion lost as waste heat. Understanding the energy balance allows one to determine the net work output per cycle by considering both the energy input and the energy rejected in each operational cycle.

Heat of Combustion

The heat of combustion is a measure of the energy released when a given volume or mass of fuel is burned completely. It provides a direct link between the energy content of the fuel and its required volume for a specified energy need, making it essential for calculating fuel consumption based on the total energy used during engine operation.

Power and Unit Conversion

Power is defined as the rate at which work is done or energy is transferred over time, typically measured in Watts (joules per second). Converting power into other units, such as horsepower, is crucial for comparing engine outputs with standard performance metrics. This concept involves using unit conversion factors to transition between different measurement systems.

Torque and Angular Velocity Relationship

In rotational dynamics, the mechanical power output of an engine is the product of torque and angular velocity. This relationship provides a way to calculate the torque exerted by the engine when the power output and engine speed are known. It is a key concept in understanding how rotational motion converts into measurable work.

Waste Heat Removal

Not all the energy produced in an engine is converted into useful mechanical work; some is inevitably lost as waste heat. Recognizing the quantity of waste heat that must be transferred out of the engine is important for the design of exhaust and cooling systems that ensure safe and efficient engine operation while preventing overheating.

Transcript

00:01 Hi everyone in this problem it is given.

00:04 Air aeroplane having multi -cylinder gasoline engine operating at frequency.

00:11 Operating frequency is given 2 ,500 revolution per minute.

00:21 In one revolution it is absorbing amount of the heat absorbed in one revolution is 7 .89 into 10 to the power 3 jule and expelling out 4 .58 into 10 to the power 3 jule.

00:46 In the first part we have to calculate how many liters of fuel that is amount of fuel required in one hour if heat convention of the fuel is 4 .03 into 10 the power 7 joules per liter.

01:30 In second part we have to calculate mechanical power output.

01:38 In third part we have to calculate the torque generated in crank and soft and deep part we have to calculate power of cooling that is exhaust.

01:53 Start solving it one by one.

01:58 In first part we will calculate amount of the heat taken in one hour.

02:06 Amount of the of heat absorbed in one hour.

02:21 That will be heat absorbed in one revolution into number of revelations in one hour.

02:50 So q total you will get, that is to be absorbed 4 .5 into 10 to the power 3 joule per revelation and number of revelation in one minute.

03:08 In one minute, in one it is completing 2 ,500 revelation.

03:13 So in one hour it will complete revelation per hour.

03:22 So on solving it total amount of heat, q total you will get 1 .18 into 10 to the power 9 jule per hour.

03:45 This is the amount of the heat required.

03:47 So amount of fuel required can be defined as total heat absorbed in one hour divided by heat convention of fuel.

04:32 This we have calculated 1 .18 into 10 to the power 9 joules per hour and heat convention is given 4 .03 into 10 to the power 7 jule per liter.

05:03 So amount of fuel we will get in one hour that is required by the engine is 29 .4 liter...

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