Question

-
9.
Rate of flow of a liquid through a capillary tube of length I and radius a under a pressure head
N n p a4
p is given by at = where n is the coefficient of viscosity of the liquid. Test the formula
dimensionally.
8 in​

Answer 1

Answer:

FLOW OF VISCOUS LIQUID THROUGH A CAPILLARY TUBE :

The velocity v at a distance y from the capillary axis for a flow of liquid of viscosity η in a capillary tube of length L and radius r under a pressure difference p across it is given by

v = ( P/4ηL) (r2 – y2 )

and the volume of liquid flowing per second is given by

Illustration : A metal plate 0.04 m2 in area is lying on a liquid layer of thickness 10-3m and coefficient of viscosity 140 poise. Calculate the horizontal force needed to move the plate with a speed of 0.040 m/s.

Solution : Area of the place A = 0.04 m2

Thickness Δx = 10-3m

Δx is the distance of the free surface with respect to the fixed surface.

Velocity gradient,

Coefficient of viscosity, η = 14kg/ms-1

Let F be the required force,

Then, F = ηA Δv/Δx

= 22.4 N

Illustration : A liquid flows through a pipe of 1.5mm radius and 15cm length under a pressure of 15,000 dyne/cm2. Calculate the rate of flow and the speed of the liquid coming out of the pipe. The coefficient of viscosity of the liquid is 1.40 centipoise.

Solution: Radius r = 1.5mm = 0.15cm

Length L = 15cm

Pressure difference, p = 15×103 dyne/cm2

Coefficient of viscosity, η = 1.40 centipoise = 0.0140 poise

Rate of flow,

= 14.19 cm3/s

Velocity,

= 200.84 cm/s