Question

На реактивном лайнере установлено 4 двигателя, каждый из которых при полной нагрузке развивает силу тяги 40 кН. Определите массу топлива, необходимого лайнеру для преодоления расстояния 150 км, если удельная теплота сгорания топлива 40МДжкг, а КПД двигателя 40%. Ответ выразите в тоннах, округлите до десятых.

Answer 1

Дано:

N=4;

F=40 кН;

s=150 км;

q=40 МДж/кг;

η=40 %;

____________

Найти: m

СИ: F=4*10⁴ Н; s=1.5*10⁵ м; q=4*10⁷ Дж/кг

Решение:

Рассчитаем полезную работу, совершаемую двигателями по перемещению лайнера:

$\displaystyle A=NFs=4*4*10^4*1.5*10^5=2.4*10^{10}$ Дж

Из определения КПД выразим полное количество теплоты:

$\displaystyle \eta=\frac{A}{Q} => Q=\frac{A}{\eta}=\frac{2.4*10^{10}}{0.4}=6*10^{10}$ Дж

Необходимая масса топлива:

$\displaystyle Q=qm => m=\frac{Q}{q}=\frac{6*10^{10}}{4*10^7}=1500$ кг или 1,5 т

Ответ: 1,5 т.

Answer 2

Calculation of Fuel Mass for the Jetliner

To determine the mass of fuel required for the jetliner to cover a distance of 150 km, we need to consider the thrust force developed by the four engines, the specific heat of combustion of the fuel, and the efficiency of the engines.

Given: - Number of engines: 4 - Thrust force developed by each engine at full load: 40 kN - Distance to be covered: 150 km - Specific heat of combustion of the fuel: 40 MJ/kg - Efficiency of the engines: 40%

Calculation Steps:

Step 1: Calculate the total thrust force developed by all four engines: - Total thrust force = Thrust force per engine * Number of engines - Total thrust force = 40 kN * 4 = 160 kN

Step 2: Calculate the work done by the engines: - Work done = Total thrust force * Distance - Work done = 160 kN * 150 km

Step 3: Convert the work done to energy: - Energy = Work done * 1000 (to convert from kN to N) - Energy = (160 kN * 150 km) * 1000

Step 4: Calculate the mass of fuel required: - Mass of fuel = Energy / Specific heat of combustion of the fuel - Mass of fuel = (160 kN * 150 km * 1000) / 40 MJ/kg

Step 5: Convert the mass of fuel to tonnes: - Mass of fuel (in tonnes) = Mass of fuel (in kg) / 1000

Calculation:

Using the given values and performing the calculations:

Step 1: Total thrust force = 40 kN * 4 = 160 kN

Step 2: Work done = 160 kN * 150 km = 24,000 kN·km

Step 3: Energy = (24,000 kN·km) * 1000 = 24,000,000 N·m

Step 4: Mass of fuel = (24,000,000 N·m) / (40 MJ/kg) = 600,000 kg

Step 5: Mass of fuel (in tonnes) = 600,000 kg / 1000 = 600 tonnes

Answer:

The jetliner would require approximately 600 tonnes of fuel to cover a distance of 150 km, assuming each of the four engines develops a thrust force of 40 kN at full load, the specific heat of combustion of the fuel is 40 MJ/kg, and the engine efficiency is 40%.