The most powerful variant of the General Electric GE90 engine (the biggest turbofan engine in the world, see below) is able to produce over 500 kN of thrust in a standstill full power test at sea level. Its exhaust speed is estimated to be 730.8 kts. Based on this data, determine the volume of air (in cubic metres) this engines takes in per second for this thrust.
To determine the volume of air the GE90 engine takes in per second for a thrust of over 500 kN, we can use the equation:
Thrust = mass flow rate * exhaust velocity
First, let's convert the thrust from kilonewtons (kN) to newtons (N):
Thrust = 500 kN * 1000 N/kN
Thrust = 500,000 N
Next, let's convert the exhaust velocity from knots (kts) to meters per second (m/s):
Exhaust speed = 730.8 kts * (1852 m/nautical mile) / (3600 s/hour)
Exhaust speed = 372.6 m/s
Now, we can rearrange the equation and solve for the mass flow rate:
mass flow rate = Thrust / exhaust velocity
mass flow rate = 500,000 N / 372.6 m/s
mass flow rate ≈ 1342.29 kg/s
The density of air at sea level is approximately 1.225 kg/m^3. To calculate the volume of air the engine takes in per second, we can divide the mass flow rate by the density:
volume flow rate = mass flow rate / air density
volume flow rate = 1342.29 kg/s / 1.225 kg/m^3
volume flow rate ≈ 1095.8 m^3/s
Therefore, the GE90 engine takes in approximately 1095.8 cubic meters of air per second for a thrust of over 500 kN.
To solve this problem, we need to use the definition of thrust, which is the force generated by the engine that propels an aircraft forward. The formula for thrust is:
Thrust = Mass flow rate * Exhaust velocity
We can rearrange this formula to solve for mass flow rate:
Mass flow rate = Thrust / Exhaust velocity
We are given the thrust and exhaust velocity, so we can plug in these values:
Mass flow rate = 500 kN / 730.8 kts = 0.6833 kg/s
Now we need to convert the mass flow rate to a volume flow rate, which is the volume of air that the engine takes in per second. To do this, we need to use the ideal gas law:
PV = nRT
where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature. Assuming that the air behaves like an ideal gas, we can rearrange this equation to solve for the volume:
V = nRT/P
We are given the pressure (sea level), gas constant (R), and temperature (assume 288 K, which is the standard temperature at sea level). We also know the mass flow rate (0.6833 kg/s), so we can calculate the number of moles of air per second:
n = mass flow rate / molar mass of air = 0.6833 kg/s / 0.02897 kg/mol = 23.586 mol/s
Putting all these values together, we get:
V = nRT/P = (23.586 mol/s)(8.314 J/mol/K)(288 K)/(101325 Pa) = 0.845 m^3/s
Therefore, the volume of air that this engine takes in per second for a thrust of 500 kN is approximately 0.845 cubic metres.