{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Error%20estimation

# Error%20estimation - coeﬃcient is given by U a pp = WC p...

This preview shows page 1. Sign up to view the full content.

Estimation of Error When calculating the expectation and variance of any nonlinear func- tion of random variables, the function must be linearized first. The mean and variance computed from the linearized expressions are only approximate and apply only in the vicinity of the state about which the variables in the function have been linearized. Assuming that the random variable are inde- pendent, the variance is expressed as Var { f ( X 1 , X 2 , · · · , X n ) } = n X i =1 ∂f ( x 1 , x 2 , · · · , x n ) ∂x i 2 μ x 1 x 2 , ··· Var { X i } A special case of this equation occurs when the original function is of the form Y = cX a 1 1 X a 2 2 · · · X a n n because then σ y μ y 2 = a 2 1 σ x 1 μ x 1 2 + a 2 2 σ x 2 μ x 2 2 + · · · + a 2 n σ x n μ x n 2 Example: Estimation of error in a Heat Transfer Coefficient Consider a laboratory experiment dealing with the unsteady-state heating of water in a steam-jacketed open kettle. The apparent overall heat transfer
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: coeﬃcient is given by U a pp = WC p A Δ T ( dT dt ) where W = weight of water, lb A = area of kettle in contact with water through which heat transfer takes place, ft 2 C p = speciﬁc heat capacity of water, BTU/(lb)( F) Δ T = temperature diﬀerence between the steam and water, F dT dt = slope at any instant of the curve of water temperature verses time. Assume that all variables except speciﬁc heat are random variables. Find the mean value of U a pp and its precision at the given condition. The measurements and estimated variance of each variable is given as W ∼ N (1200 , . 08) A ∼ N (8 . 74 , . 0225) Δ T ∼ N (60 , . 26) dT dt ∼ N (3 , . 048) 1...
View Full Document

{[ snackBarMessage ]}