Problem 3.

A force F is applied on a square plate of side L. If the percentage error in determination of L is 3% and that in F is 4%. what is the permissible error in pressure?

Solution:

The pressure is defined as the ratio of force and area:

where area of a square plate of side is . Then

We introduce the error in determination of the force and the error in determination of the length. Therefore, the force is

And the length is

We know the percentage errors of the force and the length: (4%) and (3%). Then

In the above expressions we should use the absolute values since the errors can be positive and negative.

Now we can express the pressure in terms of the errors of the force and the length:

We consider and as small parameters and use the Taylor expansion of the above expression to find the linear terms in and :

Then the error in pressure is

........................................................(1)

We know that

Then the maximum error in pressure is

(it is important that we add these two corrections). Then