Question

A 20-cm-diameter circular cover is placed over a 10-cm-diameter hole that leads into an evacuated chamber. The pressure in the chamber is 20 kPa. How much force is required to pull the cover off?

Short answer

Force needed is 638 N

Step-by-step solution

Given information

A 20-cm-diameter circular cover is placed over a 10-cm-diameter hole that leads into an evacuated chamber.

The pressure in the chamber is 20 kPa.

2Step2: Explanation

Force needed can be calculated by

Force = difference in pressure x area of plate

Force = difference in pressure x area of plate

F = (P2 -P1) x A ..............................(1)

F = (P2 -P1) x π r²

P1 = 20000 Pa

P2 = 101325 Pa

r = 0.05 m

Now substitute the values in equation (1) and calculate

F = (101325 Pa- 20000 Pa ) x 3.14 (0.05m)²= 638 N

Force needed is 638 N