A barometer contains two uniform capillries of radii `1.44 xx 10^(-3)m` and `7.2 xx 10^(-4)m`. If the height of the liquid in the narrow tube is `0.2 m` more than that in the wide tube, calculate the true pressure difference. Density of liquid `= 10^(3) kg//m^(3)`, surface tension `= 72 xx 10^(-3) N//m` and `g = m//s^(2)`.

Explanation

Let the pressure in the wide and norrow capillaries of radii `r_(1)` and `r_(2)` respectively be `P_(1)` and `P_(2)`.
Then pressure just below the meniscus in the wide and narrow tubes respectively are
`(P_(1) - (2T)/(r_(1)))` and `(P_(2) - (2T)/(r_(2)))` [excess pressure `= (2T)/(r)`]
Difference in these pressures `= (P_(1) - (2T)/(r_(1))) -(P_(2) - (2T)/(r_(2))) = hrhog`
`:.` True pressure difference `= P_(1) - P_(2)`
`= 2rhog + 2T((1)/(r_(1)) - (1)/(r_(2)))`
`= 0.2 xx 10^(3) xx 9.8 + 2 xx 72 xx 10^(-3) [(1)/(1.44 xx 10^(-3)) - (1)/(7.2 xx 10^(-4))]`
`= 1.86 xx 10^(3) = 1860 N//m^(2)`