Question

The engine displacement of an automobile is the volume through which the piston moves from high to low position. If an engine has n cylinders, the displacement is D = pi(bore/2)^2 • stroke • n, where the bore is the diameter of the cylinder and stroke is the length of the piston's travel.

If bore = k/2 and stroke = h, simplify the expression, D, in terms of k and h for 8 cylinders.

If the bore is 4 inches, the stroke is 3.4 inches, and the engine has four cylinders, what is the displacement? Round your answer to the nearest tenth of a cubic inch.

Answer 1

`85.4` cubic inch

Explanation:

Given-

Displacement =
`\pi ((bore)/(2) )^2 * stroke * n`

Now,

bore is represented as
`(k)/(2)`

and stroke is represented as
`h`

and number of cylindres "n"
`= 8`

Substituting these values in above equation, we get -

Displacement
`= \pi (((k)/(2) )/(2))^2*h*8\\= \pi (k^2)/(16) * h* 8\\= (\pi* k^2*h)/(2)`

Now substituting the given values, in above equation we get -

Displacement
`= (\pi* 4^2*3.4 )/(2)\\= (\3.14* 16*3.4 )/(2) \\ = 85.408\\= 85.41= 85.4`cubic inch

Answer 2

• D = (π/2)hk² . . . . for 8 cylinders
• D = 170.9 in³

Explanation:

Substituting the given expressions for bore and stroke and 8 cylinders, you have ...

... D = π((k/2)/2)^2 · h · 8

... D = (π/2)hk^2 . . . . simplified expression for 8 cylinders

_____

For bore = 4 in, stroke = 3.4 in, n = 4, the displacement is ...

... D = π(4 in/2)^2 · (3.4 in) · 4 = 54.4π in^3

... D ≈ 170.9 in^3