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A horizontal pipe of varying cross-secti...

A horizontal pipe of varying cross-sectional area carries water flowing at a constant rate. The pressure at sections (1) and (2) are `50 cm` and `20 cm` of `Hg`. If the velocity of section (1) is `5 m//s`, what is the velocity of section (2). Also determine the ratio of areas at sections (1) and (2) (as shown in Fig.

Text Solution

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Since the flow is horizontal, so the reduced form of bernoullis' equation can be applied as
`P_(1)+1/2rhov_(1)^(2)=P_(2)+1/2rhov_(2)^(2)`
given `P_(1)=50xx13.6xx1000=6.8xx10^(5)dyn//cm^(2)`
and `P_(2) =20xx13.6xx1000=2.72xx10^(5)dyn//cm^(2)`
and `rho=1g//cc` and `v_(1)=500cm//s`
`:. 6.8xx10^(5)+1/2xx1xx(500)^(2)=2.72xx10^(5)xx1/2xx1xxv_(2)^(2)`
`=1/2(v_(2)^(2)-250000)=4.08xx10^(5)impliesv_(2)=10.25ms^(-1)`
From the priciple of continuity `a_(1)v_(1)=a_(2)v_(2)`
`(a_(1))/(a_(2))=(v_(2))/(v_(1))=10.25/5=41/20`
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