Question

A capillary tube 1mm in diameter and 20 cm in length is fitted horizontally to a vessel kept full of alcohol. The depth of the center of capillary tube below the surface of alcohol is 20 cm. If the viscosity and density of alcohol are 0.012 cha unit and 0.8 gcm^-3 respectively. Find the amount of the alcohol that will flow out in 5 minutes. Given that g=980 cms^-2

Answer 1

The amount of the alcohol that will flow out in 5 minutes is 38.4 gms

Explanation:

Pressure difference , p = ρgh = 0.8 x 980 x 20 = 15680 dyne/cm²

diameter, d = 1 mm

=> radius, r = 0.5 mm = 0.05 cm

viscosity, v = 0.012

length , L = 20 cm

we know that volume of liquid flowing per second through a capillary is given by,

Q = $\frac{\pi p r^4}{8vL}$

= (3.14 x 15680 x 0.05⁴)/ 8x0.012x20

= 0.16 cm³

This is the volume of alcohol flowing in 1 sec

=> volume of alcohol to flow in 5 minutes

= 0.16 x 5 x 60

= 48 cm³

mass = volume x density

= 48 x 0.8

= 38.4 g

Hence the amount of the alcohol that will flow out in 5 minutes is 38.4 gms