Question

When gasoline is burned in the cylinder of an engine, it creates a high pressure that pushes the piston. If the pressure is 100.0 psi and it moves a 3.0 in diameter piston a distance of 5.0 cm in 0.10 seconds, how much horsepower does this action produce?

Answer 1

`\dot W=2.1074\ hp`

Step-by-step explanation:

Given:

• pressure on the piston,
  `P=100\ psi=689476\ Pa`

• diameter of the piston,
  `d=3\ in=0.0762\ m`

• displacement of the piston,
  `s=0.05\ m`

• time taken in the piston displacement,
  `t=0.1\ s`

Now, we find the force on the piston:

`F=P.A`

where, A = area upon which pressure acts

`A=\pi.(d^2)/(4)`

`A=\pi.(0.0762^2)/(4)`

`A=0.00456\ m^2`

`\therefore F=689476* 0.00456`

`F=3144.2638\ N`

we know that Power is given as:

`\dot W=(F.s)/(t)`

`\dot W=(3144.2638* 0.05)/(0.1)`

`\dot W=1572.1319\ W`

`\dot W=2.1074\ hp`