Thread: determine approximate percentage error using binomial expansion

The shear stress τ in a shaft of diameter
D under a torque T is given by:
τ = kT
πD^3 .
Determine the approximate percentage error
in calculating τ if T is measured 3% too
small and D 1.5% too large.

(answer 7.5% decrease)


this is a question from J bird engineering mathematics book. it gives the answer but i need to know how to do the method.

any help much appreciated

Hello decoy808

Originally Posted by decoy808

The shear stress τ in a shaft of diameter
D under a torque T is given by:
τ = kT
πD^3 .
Determine the approximate percentage error
in calculating τ if T is measured 3% too
small and D 1.5% too large.

(answer 7.5% decrease)


this is a question from J bird engineering mathematics book. it gives the answer but i need to know how to do the method.

any help much appreciated

If , and and increase by small amounts and , then







, ignoring higher powers of , which we may do for small increases in

the fractional increase in the fractional increase in .

It is very easy show that this may be extended to a formula for which involves powers of any number of variables.

So, using the same method you may prove that if , then



With the percentage errors you have been given

and

So %

Grandad