Unformatted text preview: ing V1, we solve these for V2 or Q in terms of the pressure change p1
Q
A2 2(p1 p2)
4
(1 D2/D4) V2 p2: 1/2 (6.123) But this is surely inaccurate because we have neglected friction in a duct flow, where
we know friction will be very important. Nor do we want to get into the business of
measuring vena contracta ratios D2/d for use in (6.123). Therefore we assume that
D2/D
and then calibrate the device to fit the relation
Q AtVt 2(p1
1 Cd At p2)/ 1/2 (6.124) 4 where subscript t denotes the throat of the obstruction. The dimensionless discharge
coefficient Cd accounts for the discrepancies in the approximate analysis. By dimensional analysis for a given design we expect
Cd f( , ReD) where ReD The geometric factor involving V1D (6.125) in (6.124) is called the velocityofapproach factor
E 4 (1 ) 1/2 (6.126) One can also group Cd and E in Eq. (6.124) to form the dimensionless flow coefficient
Cd CdE (6.127) 4 1/2 (1 ) Thus Eq. (6.124) can be written in the equivalent form
Q At 2(p1 p2) 1/2 (6.128) Obviously the flow coefficient is correlated in the same manner:
f( , ReD) (6.129) Occasionally one uses the throat Reynolds number instead of the approach Reynolds
number
Red Vtd ReD (6.130) Since the design parameters are assumed known, the correlation of from Eq. (6.129)
or of Cd fro...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
 Spring '08
 Sakar

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