Water at 60 degree F flows steadily through a horizontal circular divergent duct
ID: 1823101 • Letter: W
Question
Water at 60 degree F flows steadily through a horizontal circular divergent duct and discharges into the atmosphere as shown. A manometer with a fluid of SG = 2. 0 is placed between the two cross-sections with diameters D1 = 0. 5 ft and D2 = 0. 7 ft. Assuming inviscid flow, determine: The pressure difference (P2 - P1) at the centerline between these two sections. The velocities V1 and V2 at the two sections. The volume flow rate Q, and the velocity V3 at the exit section with diameter D3 = 1 ft.Explanation / Answer
a) P2 - P1 = 2 x 1000.g.h
= 2000 x 32.174 x 0.2 = 12.87 x 103
b) P1/ + V12/2 + g.z1 = P2/ + V22/2 + g.z2
z1 = z2
A1.V1 = A2.V2
V1 = A2/A1 . V2
= 0.72/0.52 . V2
V1 = 1.96 V2
( P2 - P1)/ = (V12 - V22 )/2
12.87 x 1000 / 1000 = [ (1.96V2) 2 - V22 ]/ 2
V2 = 3 ft/s
V1 = 1.96 x V2 = 5.9 ft/s
c) Q = A.V = A2.V2 = /4 x 0.72 x 3 = 1.154
NOW,
Q = A3.V3 = 1.154 = /4 x 12 x V3
V3 = 1.47 ft/s
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