THEORY: When a liquid flows through a capillary tube of length l and radius r then the volume of liquid flowing per second is given by,
V = \( (πPr^4)/8ηl \)
where,
η = Co-effiecient of viscosity
P = Pressure difference between two ends = hρg
g = acceleration due to gravity
η = \( (πgρr^4)/8l (h/V) \)
where,
h = difference in height between the two arms of the apparatus = (h_{2}-h_{1})
ρ = density of liquid
Apparatus: Viscosity apparatus, Travelling microscope, cathetometer, measuring cylinder, stop watch.
Procedure:
- Measure the length of the capillary tube with the help of a metre scale.
- Measure the radius of the sample capillary tube with the help of the travelling microscope. Determine the Vernier Constant of the microscope. Place the tube on a stand facing the microscope. Focus the orifice. Take reading of the top, down and right ends of the circular orifice.
- Place the water tank of the viscosity apparatus at a certain level. Allow the water to come out of the tube at a very slow rate (drop by drop). Wait until the water levels at two arms of the manometer take steady values.
- Collect water from the output end in a measuring cylinder for a fixed time, say T = 4 minutes. Measure the volume. From that calculate the volume of water collected per second.
- Change the height of the water tank several times and repeat steps 3 and 4.
- Draw a graph with h in abscissa and V in ordinate. The curve should be a straight line passing through the orifice. If there is a curvature for high values of h, use the linear portion to calculate the slope .
Experimental Results:
- Vernier constant of the travelling microscope:
- Measurement of radius of Capillary tube:
No. of obs. | Top (Y_{1}) | Bottom(Y_{2}) | Left(Y_{3}) | Right(Y_{4}) | D_{1} = (Y_{1}~Y_{2}) cm. | D_{2} = (Y_{3}~Y_{4}) cm. | D = cm. | Radius (r) = cm. | Mean radius (r) cm. | ||||||||
MSR | VSR | Total | MSR | VSR | Total | MSR | VSR | Total | MSR | VSR | Total | ||||||
- Detemination of (V/h) :
No. of Obs. | Reading of the manometer in cm. | Volume of water collected per minute | Volume of water collected per second (cc/sec.) | |||||
h_{1} cm. | h_{2} cm. | h = (h_{2}-h_{1}) cm. | I | II | III | IV | ||
Calculation:
Percentage error:
η = \( (πgρr^4)/8l (h/V) \)
\( δη/η=δt/t+δh/h+δV/V \)
Conclusion: