Chapt06

637 a complete flowmeter system using a laminar flow

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 velocity-of-approach 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...
View Full Document

Ask a homework question - tutors are online