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Viscosity of liquid

                                                          viscosity of liquid 

purpose: to determine the viscosity of medium by using small sphere falls with a constant terminal velocity .

apparatus:

1.along glass tube 50 cm long closed at one end.

2.glycerine.

3.meter scale.

4. small sphere.

5.magnet.

6.stop-watch.

7.rubber bands.

method:

1.adjest the distance between the rubber bands.

2.record the distance (h) between them about 30 cm.

3.droping the sphere centrally down the tube and with stop-watch find the time it takes to traverse the distance between the rubber  bands.     

4. obtain two values of the time of the fall.

5. repeat the experience for the different values of (h) and obtain two values of the time of fall for each new distance apart.

reading and calculation:

1.plot the graph with value of (h)(cm)on y-axis against the value of t(sec) on x-axis.

2.from the graph calculate the terminal velocity.

v=h/t=velocity (cm/sec).

3.to deduce the viscosity (?) for liquid,use the following equation

?=g(p-?).d²/18.v

g=9.8 cm/sec²

p=density of sphere`=7.8 gm/cm³

d=diameter of sphere

? =density of liquid =1.231 gm/cm³

v=velocity (slope)

medical  application

equation is valid only for spherical particles ,however ,we can use it as a guide to the behavior of a particles with amore complicated shape.

in some of disease such as rheumatic fever ,rheumatic heart disease and gout ,the red blood cell clump together and the effective radius increase ,thus an increase d sedimentation velocity occurs. in other disease such as hemolytic jaundice and sickle  cell anemia ,the red blood cells change shape or break. the radius decreases thus the rate of sedimentation velocity of these cells is slower   than normal .determining the sedimentation rate of red blood cells is a simple routine clinical laboratory test.

a related medical test that also depends on equation, is determination of the hematocrit ,the percent of red blood cells in the blood. since the sedimentation velocity is proportional to the gravitational acceleration ,it can be greatly enhanced if the acceleration is increased .we can increase g by means of a centrifuge ,which provides an effective acceleration  g=4 ?² f² r ,where f is the rotation rate in revolution per second  and r is the position on the radius of the centrifuge where the solution is located.

since the packing of the red blood cells take place in the centrifuge ,the hematocrit obviously depends upon the radius of the centrifuge and the speed and the duration of centrifugation .the increase of any of these leads to more dense packing of the red blood cells or a smaller hematocrit .one standard method utilizes centrifugation for 30 min at 3000 rpm with r =22cm,anormal hematocrit is 40 to 60 , a value lower than 40 indicates anemia ,a high value may indicate polycythemia vera.