Error%20estimation

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

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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 2 ³ ³ ³ ³ 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 2 = a 2 1 ± σ x 1 μ x 1 ² 2 + a 2 2 ± σ x 2 μ x 2 ² 2 + ··· + a 2 n ± σ x n μ x n ² 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
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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...
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This note was uploaded on 04/07/2008 for the course CHE 356 taught by Professor Dunia during the Spring '08 term at University of Texas.

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