The cross sectional area of a horizontal pipe is decreasing from 5 xx 10^(-2) m^2" to "1 xx 10^(-2) m^2?. Water is flowing with speed of 5 m/s through this pipe with a pressure of 5 xx 10^5 Pa through the larger cross section. The pressure at the smaller cross section of the pipe is n xx 10^(4) Pa. Find the value of n.

The cross sectional area of a horizontal pipe is decreasing from 5 xx

1.	The cross sectional area of a horizontal pipe is decreasing from 5 xx 10^(-2) m^2" to "1 xx 10^(-2) m^2?. Water is flowing with speed of 5 m/s through this pipe with a pressure of 5 xx 10^5 Pa through the larger cross section. The pressure at the smaller cross section of the pipe is n xx 10^(4) Pa. Find the value of n.
Answer» <P> Solution :`a_(1)=5 xx 10^(-2) m^(2)` `a_(2)=10^(-2) m^(2)` `v_(1)=5m//s` `p_(1)=5 xx 10^(5) pa` ACCORDING to equation of continuity `a_(1)v_(1)=a_(2)v_(2)` `v_(2)=(a_(1)v_(1))/(a_(2))` `=(5 xx 10^(-2) xx 5)/(10^(-2)) =25m//s` Accoring to Bernoulli.s theorem `p_(1)+1/2 pv_(1)^(2)=p_(2)+1/pv_(2)^(2)` `p_(2)=p_(1)+1/2 PV(1)^(2)-1/2pv_(2)^(2)` `p_(2)=p_(2)+1/2p(v_(1)^(2)-v_(2)^(2))` `=5 xx 10^(5) +1/2 xx 1000 ((5)^(2)-(25)^(2))` `=5 xx 10^(5) +500 (25-625)` `=5 xx 10^(5) +500 (-600)` =500000-300000=200000 Pa