A siphon has a uniform circular base of diameter `8//sqrt(pi) cm` with its crest `A, 1.8 m` above the water level vessel `B` is of large cross section (`g= 10 m//s^(2)` and atmospheric pressure `P_(0) = 10^(5) N//m^(2))`.

Answer

`6sqrt(2)m//s, (b) 9.6 xx 10^(-3)M^(3)//sec,(c )4.6xx10^(4)N//m^(2)`

Explanation

(a) `v_(2) = sqrt(2gh_(2)) " "implies v_(2) = sqrt(2xx10xx3.6)" "v_(2)=6sqrt(2)m//s`
(b) `V = av_(2)" "impliesV=pi((4xx10^(-2))/(sqrt(pi)))^(2)xx6sqrt(2)m^(3)//s" "impliesV=9.6sqrt(2)m^(3)//s`
(c ) Applying Bernouli's theorem between A and out let
`P_(A)+(1)/(2)rhov_(A)^(2)+rhog(h_(1)+h_(2))=P_(0)+(1)/(2)rhov_(2)^(2)+0" "...(1)`
From conservation of mass
`((dm)/(dt))_(A)=((dm)/(dt))_("outlet")`
`(rhoAv_(A))=(rhoAv_(B))`
`v_(A)=v_(B)" "....(2)`
From (1) and (2)
`P_(A)+rhog(h_(1)+h_(2))=P_(0)" "impliesP_(A)=P_(0)-rhog(h_(1)+h_(2))`
`=10^(5)-10^(3)xx10xx5.4" "=4.6xx10^(4)N//m^(2)`