Question

Airplane takeoff from an aircraft carrier is assisted by a steam-driven piston/cylinder assembly. A 17,500 kg airplane should accelerate from 0 to 30 m/s with 30% of its energy coming from the steam piston. The pressure in the cylinder starts at 10 bar (1000 kPa), dropping linearly with volume to reach 2 bar (200 kPa) at the end of the process. What is the needed piston displacement volume in m3?

Answer 1

The volume =
`V=3.93m^3`

Step-by-step explanation:

Given Data:

mass = m = 17500 kg

initial velocity = Vi = 0 m/s

Final velocity = Vf = 30 m/s

Initial Pressure = Pi = 1000KPa

FInal Pressure = Pf = 200 Kpa

Required?

Piston Displacement Volume = V = ?

SOlution

We will first find out the change in kinetic energy and from that energy, we will calculate the volume required.

as we know:

`E = 1/2 m (Vf-Vi)^2=1/2 * 17500*(30-0)^2\\E=7875KJ`

But it is mentioned that only 30 percent of this energy comes from steam driven piston.

therefore,

`E(from steam)= 0.30 * E\\E(from steam) = 0.30 * 7875\\E(from steam) = 2362.5KJ`

No we will calculate the volume from energy equation

`Energy = Average Pressure * Volume`

Now

`Average Pressure = (1000+200)/2 = 1200/2 = 600 KPa`

Substituting this value

`Energy = Average Pressure * Volume\\E = P * V\\V = E / P\\V=2362500 J/600000Pa\\V= 3.93m^3`