Question

The limbs of a manometer consists of uniform capillary tubes of radii `1.44 xx 10^(-3)m` and `7.2 xx 10^(4 )m`. If the level of the liquid in the narrower tube stands 0.2 m above that in the broader tube, pressure difference between A and B is found to be `310lambda N//m^(2)`. Here `lambda` is an integer. Find `lambda` (density = `10^3 kg//m^3`, surface tension = `72 xx 10^(-3) N//m`). (take `g = 9.8 m//s^2`)

Answer 1

`r_(1)=1.44xx10^(-3) m , r_(2)=0.72xx10^(-3) m`
Equating pressures at points (B) and C
`P_(A)-(2sigma)/(r_(2))+(0.2) rhog=P_(C)` and `P_(B)-(2sigma)/(r_(1)) =P_(C)`
so `P_(B)-P_(A)=2 sigma(1/(r_(1))-1/(r_(2)))+0.2 rhog`
`=2xx72xx10^(-3) N/mp[(10^(-3))/1.44-(10^(3))/0.72]+(0.2)xx10^(3)xx938`
`=(144xx(-0.72))/(1.44xx0.72)+1960 =-100 +1960 =1860 N//m^(2)`.