16.       A liquid of density 900 kg/m³ is filled in a cylindrical tank of upper radius 0.9 m and lower radius 0.3 m. A capillary tube of length l is attached at the bottom of the tank as shown in the figure. The capillary has outer radius 0.002 m and inner


radius a. When pressure P is applied at the top of the tank volume flow rate of the liquid is 8 × 10^-6 m³/s and if capillary tube is detached, the liquid comes out from the tank with a velocity 10 m/s. Determine the coefficient of viscosity of the liquid.
            [Given : pa² = 10^-6 m³ and a² / l = 2 × 10^-6 m]

FOR CALCULATING THE PRESSURE DROP ACROSS THE CAPILLARY TUBE WE CAN SIMPLY APPLY BERNOULLI'S EQUATION B/W THE TWO ENDS OF THE CAPILLARY TUBE AND FOR THAT WE DONT NEED THE HEIGHT "h" AND THE VALUES OF THE RADII "0.3" AND "0.9" IN THE SOLTUION IT IS OTHERWISE PLZ CONFIRM...

Mayank Kumar Jha, 13 years ago

Grade:11

1 Answers

SAGAR SINGH - IIT DELHI

878 Points

13 years ago

Dear student,

For laminar, non-pulsatile fluid flow through a uniform straight pipe, the flow rate (volume per unit time) is given by Poiseuille's Equation:

F = ΔP π r⁴ / 8 η l.

Obviously, the use of Poiseuille's Equation on the human circulatory system is highly suspect. While the flow is essentially laminar outside of the capillaries, it is definitely pulsatile throughout the arterial subsystem. In addition, the equation is based on the parabolic velocity gradient discussed in the last section. But since pressure waves in arterial walls propagate more quickly than those in blood, the velocity profile is more uniform than parabolic. Beyond that, Poiseuille's Equation assumes a constant viscosity, whereas the viscosity of blood actually changes with velocity, since blood is not a uniform fluid. In fact, the viscosity is much lower in the capillaries than in the rest of the system, since the red blood cells line up in single file to pass through them. On top of everything else, the blood vessels are not straight, uniform pipes!