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

Answer:

$85.4$ cubic inch

Step-by-step explanation:

Given-

Displacement = $\pi (\frac{bore}{2} )^2 * stroke * n$

Now,

bore is represented as $\frac{k}{2}$

and stroke is represented as $h$

and number of cylindres "n"$= 8$

Substituting these values in above equation, we get -

Displacement $= \pi (\frac{\frac{k}{2} }{2})^2*h*8\\= \pi \frac{k^2}{16} * h* 8\\= \frac{\pi* k^2*h}{2}$

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

Displacement $= \frac{\pi* 4^2*3.4 }{2}\\= \frac{\3.14* 16*3.4 }{2} \\ = 85.408\\= 85.41= 85.4$cubic inch

Answer 2

Answer:

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

Step-by-step 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