Three capillary tubes of same length but internal radii 0.3 mm, 0.45 mm and 0.6 mm are connected in series and a liquid flows steadily through them. If the pressure difference across the third capillary is 8.1 mm of mercury, the pressure difference across the first capillary (in mm of mercury) is

Options

A. 16.2
B. 32.4
C. 129.6
D. 2.025

Answer

C

Explanation

We know that the equation,
`(Q)/( t) = (pi rho r^4)/( 8 eta l)`
Here, pressure difference
`p prop (1)/(r^4)`
`p prop r^(-4)`
`(p_1)/(p_3) = ((r_3)/(r_1) )^4`
`(p_1)/( 8.1) = ((0.6)/( 0.3))^4`
`p_1 = 8.1 xx 16 = 129.6`