Question

To study the flow of a liquied through a narrow tube, the following formula is used :` eta = (pi)/(8) (Pr^4)/(VI),` where letters have their usual meaning. The value of P, r, V and I are 76 cm of Hg col. `0.28 cm, 1.2 cm^3 s^(-1) and 18.2cm` respectively. If these quantities are measured to the accuracy of `0.1 cm of Hg col., 0.01 cm, 0.1 cm^3 s^(-1)` and 0.1 cm respectively, find the percentage error in the value of `eta.`

Answer 1

Here, ` P =76cm` of `Hg col. DeltaP = 0.1 cm`
` r= 0.28 cm Delta = 0.01 cm`
`V = 1.2 cm^3 s^(-1) DeltaV = 0.1 cm^3 s^(-1)`
`I =18.2 cm DeltaI = 0.1 cm`
From `eta = (pi)/(8) (Pr^4)/(VI)`
`(Delta eta)/(eta) = (DeltaP)/(P) + 4(Deltar)/(r ) +(DeltaV)/(V) + (DeltaI)/(I) = (0.1)/(76) + (4(0.01))/(0.28) +(0.1)/(1.2) +(0.1)/(18.2)`
` = 0.0013 + 0.1428 + 0.0833 + 0.0054 = 0.2328`
`:. (Delta eta)/(eta)xx100 = 0.2328xx100 = 23.28%`