Measurement of Air Viscosity

Apparatus: pipe, blower, scanning valve, digital manometer

Introduction: For fully developed laminar flow of air (viscosity,) through a circular tube of diameter d, the pressure gradient is a constant and related to the mean flow rate Q according to the formula

4

128

d

Q

dx

dp

Pressure taps located on the tube surface determine the pressure drop along its length. The mean flow rate is measured using a rotameter. In the early part of the tube, pressure gradient is not a constant due to flow development effects.

Variation of pressure with distance in developing and fully developed flow in a tube.

p

x Xd

Developing Flow

Developed Flow

Procedure:

1. Open the blower such that the suction side of a blower draws air through a

long tube.

2. Adjust the mean flow rate (Q) using variac. Experiment has to be done for

three different values of mean flow rate.

3. Open the pressure taps from 1 to 10 one by one and measure the reading

using digital manometer for each one of them once the reading gets

stabilized.

4. Repeat the above steps for 2 other readings of mean flow rate.

Observation:

Distance between two points-10 cm

Room temperature-19°C

𝑄2

𝑄1= √

𝑇1

𝑇2

(Pressure in mm H2O)

S.No Q(div) Q(ml/min) -dP/dx (Pa/m) μ (kg/m-s)

1 74 1605.5 26.67 5.87051E-05

2 63 1304.4 27.5 7.45049E-05

3 44 903.1 17.5 6.84802E-05

Sr.no Q(in ml/min)

(T=21°C) Q(in ml/min)

(T=19°C) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

1 1600 1605.5 -6.6 -6.5 -6.2 -5.8 -5.4 -4.9 -4.3 -4.2 -3.9 -3.5

2 1300 1304.4 -5.2 -5.0 -4.7 -4.3 -4.1 -3.9 -3.6 -3.3 -2.9 -2.8

3 900 903.1 -3.3 -3.1 -3.0 -2.8 -2.6 -2.4 -2.2 -2.1 -1.9 -1.7

Discussion

1) Do not take readings for very high mean speed of air, otherwise reading will

be incorrect.

2) In the early part of the tube, pressure gradient is not a constant due to flow

development effects. Therefore, measure pressure gradient and viscosity

beyond the development length xd.

3) Allow the manometer to stabilize to get correct reading.

4) The rotameter is calibrated at 21oC and hence its reading must be corrected

for room temperature changes.