Ae104a10_solutions_2

Ae104a10_solutions_2 - Ae/APh 104a Homework Solution Set #2...

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Unformatted text preview: Ae/APh 104a Homework Solution Set #2 Issued: October 12, 2010 1/3 Hot wire (i) (a) To find the relationship between the mean voltage, E w , the mean fluid temperature T a and the mean flow velocity U , substitute for h in equation (2) to get E 2 w R w = πd w l ( T w- T a )( A + BU n ) and E w = p R w πd w l ( T w- T a )( A + BU n ). Find expressions for (b) the sensitivity, S u , of the fluctuating voltage output from the wire seg- ment, e w , to a small fluctuation in velocity, Δ U The sensitivity S u relates small changes in the voltage to small changes in ve- locity, i.e. e w As given in lecture notes: S u = ∂E w ∂U = 0 . 5 q R w πd w l ( T w- T a )( A + BU n ) BnU n- 1 ( T w- T a ) S u = 0 . 5 BnU n- 1 q R w πd w l ( T w- T a ) A + BU n = 0 . 5 BnU n- 1 E w A + BU n . (c) the sensitivity, S t , of the fluctuating voltage output from the wire seg- ment, e w , to a small fluctuation in fluid temperature, Δ T a , S T = ∂E w ∂T a =- . 5 q R w πd w l ( T w- T a )( A + BU n ) ( A + BU n S T =- . 5 q R w πd w l ( A + BU n ) T w- T a =- . 5 E w T w- T a such that e w may be written as follows: e w = S u Δ U + S t Δ T a . (1) 1 (ii) To reduce the influence of temperature fluctuations at a given U , you need to reduce S T relative to S U , i.e. you want S T /S U 1. S T S U =- . 5 E w T w- T a * 2 A + BU n BnU n- 1 E w =- 1 BnU n- 1 A + BU n T w- T a Since U is fixed and you are told that A and B are only weak functions of temperature, you can make S T /S U small by making ( T w- T a ) large, so for a given experiment (ambient temperature) you need to maximize T w and run the wire hot....
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This note was uploaded on 01/05/2012 for the course AE 104a taught by Professor List during the Fall '09 term at Caltech.

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Ae104a10_solutions_2 - Ae/APh 104a Homework Solution Set #2...

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