Question

A circular piston exerts a pressure of 80 k Pa on a fluid, when the force applied to the piston is 0.2kN. What is the diameter of the piston ?

Answer 1

`P = F/A` rearranged for area, A. You then need to find the diameter from `A = pi r^2` remembering to double the radius to get diameter.

Explanation:

A = `F/P= 200/80000`

A = `0.0025 m^2`

r = `sqrt(A/pi)` = `sqrt(0.0025/pi`

r = 0.028 `m`

D = 2r = 0.056 m

Answer 2

The diameter is 0.056 m.

Explanation:

Pressure is force divided by area.
Therefore, by the manipulations of algebra, area = force/pressure.

So the area of the piston is given by
`"area" = (0.2 kN)/(80 k Pa) = (0.2*cancel(10^3) cancel(N))/(80*cancel(10^3) cancel(N)/m^2) = 0.0025 m^2`

To find diameter we first need to get the radius using the formula for the area of a circle.
area = `pi*r^2 to` from that, we can obtain
`r = sqrt("area"/pi) = sqrt((0.0025 m^2)/pi) = 0.028 m`

So the diameter is 0.056 m.

Or 5.6 cm if you prefer.

I hope this helps,
Steve