Error Propagation

Associated with each measured variable is an uncertainty originating from scatter. Uncertainty in universal constants such as acceleration due to gravity and fluid properties can be treated as negligible in comparison to . It is quite common to construct a new quantity from the measured quantities . For example, a combination of pitot static tube and manometer measures a pressure difference () and velocity () is recovered through a square root formula. It is of interest to determine the uncertainty in terms of those in , namely . Since

the following mathematical identity holds:

In most applications, thus determined is substantially larger than the true uncertainty. A closer unbiased estimate used in engineering is

(1)

In many instances, the partial derivative of function with is of order unity; in any case it serves effectively as a scale factor. Hence, for each , and Equation 1 is called the error propagation formula.