Name:_________________

Lab Section__________________ Date:_________

ME4751, Energy Systems Laboratory Measurement of Viscosity and Density of Fluid Objective: The objective of this experiment is to measure the absolute (dynamic or molecular) viscosity and the kinematic viscosity of a fluid and compare with the existing data when possible. Theory: External force is required to move a solid object in a viscous fluid. This is due to the shear stress created by the fluid on the solid surface. The shear stress is the force per unit area and is proportional to the absolute viscosity of the fluid and the velocity gradient at the solid surface,




(1)



The force required to rotate a cylinder in a viscous fluid is approximately given by   



(2)

In Eq. (2), A is the surface area, r0 is the radius of the cylinder,  is the angular velocity and “b” is the normal distance from the cylinder surface to the undisturbed fluid. (Fig. 1) Solving for the viscosity from Eq. (2), 

   ~,   

!", !#! $%", !&

(3)

The kinematic viscosity is defined by '  /)

(4)

Therefore one can determine the kinematic viscosity if the density is known. The density of fluid can be determined by using the hydrometer. This instrument uses the hydrostatic force equilibrium as shown in Fig. 2. At the equilibrium, weight of the hydrometer is balanced by the buoyancy force   )*

(5)

In Eq. (5), “m” is the mass of the hydrometer and “V” is the volume of fluid displaced by the hydrometer, that is the volume of the hydrometer submerged in the fluid. Solving for the density )

+ ,



+ -

(6)

For a given hydrometer, m (mass) and A (cross section) are known and reading the value of “x” gives the density. For the hydrometer, it is calibrated such the “x” value on the hydrometer is the density of the fluid.

The kinematic viscosity of the fluid is also measured directly by using the principle of laminar flow in a smooth pipe of small diameter. The average velocity of free falling laminar flow in a smooth vertical pipe ( ө=90o) is given by (Fig. 3) *

)" . ".  32 32'

Solving for the kinematic viscosity 1 2

'  3., 

1 2 4 3. 5

 , &

(7)

In Eq. (7), t is the time the fluid travels the distance L. The kinematic viscosity is directly proportional to the time.

 r0 b

fluid ρ,μ

Figure 1 Rotating cylinder in a viscous fluid

free surface

), g

x

mg

buoyancy force

Figure 2. Hydrostatic force equilibrium

smooth pipe, dia=d , ) p1

L

g

ө p2

Figure 3. Gravity induced (p1=p2) laminar flow in a smooth inclined pipe

Experiment: For a selected fluid at the room temperature. For the measurement of absolute viscosity, the Brookfield Viscometer will be used. The principle of this instrument was discussed qualitatively. To use this instrument properly, follow the steps carefully. 1. Select a suitable spindle and attach it to the viscometer lower shaft. Gently tight the screw left handed way. Do not exert force on the shaft. 2. Place the viscometer on the stand and raise the fluid level until the surface of the fluid is at the center of the immersion groove on the shaft of the spindle. 3. Select the rotational speed by turning the knob on the viscometer. 4. Turn the motor switch on. 5. Allow sufficient time to reach a steady state before reading the viscometer dial. The time required for stabilization depends on the fluid, rotational speed and the spindle type. 6. To take reading, depress the clutch lever and hold it in the down position. With the lever still depressed, move the motor switch to the “off” position. Adjust the dial position, if necessary, to allow the red pointer to appear in the viscometer window. Measure the fluid temperature. 7. Remove the spindle and wipe clean the fluid. 8. The absolute viscosity is obtained by multiplying the reading by the factor appropriate to the viscometer model/spindle type/rotational speed used. Instructor will provide the factor from the manufacturer’s manual. The unit of absolute viscosity is centipoises (cP), in cgs unit system. Convert the unit to SI system by using the conversion factor, 1 cP=10-3 kg/m.s. 9. Fill in the data in table 1. Table 1. Absolute viscosity measurement fluid

Temperature (0C)

Spindle type

Dial reading

Factor (from chart)

Absolute viscosity (cP)

Absolute viscosity (kg/m.s)

Available data (kg/m.s)

For the measurement of density, Select an appropriate hydrometer and insert it into the selected fluid. Read the density directly off the scale on the hydrometer. The unit is kg/m3. Fill in the table 2.

fluid

Table 2. Density measurement Temperature (0C) Measured density(kg/m^3)

Available data (kg/m^3)

For measurement of kinematic viscosity, Canon-Fenske Routine Viscometer will be used. The principle of capillary type viscometer was presented qualitatively. The steps to use this instrument are: 1. Select an appropriate size viscometer. 2. Fill the tube with the fluid. (Instructor will show a proper way to do this step.) 3. Place the viscometer vertically in the liquid bath or on a stand.

4. Measure the elapsed time the fluid flows freely between two positions marked in the viscometer using a stop watch. Repeat this twice and take the average time. 5. Clean the viscometer using solvent and water and blow dry it. 6. Calculate the kinematic viscosity by multiplying an appropriate constant to the elapsed time(s). Instructor will provide this information from the manufacturer’s manual. The unit is in centistokes (cSt) in the cgs system. Convert the unit to SI system by using 1 cSt=10-6 m2/s. 7. Compare with the kinematic viscosity obtained by using Eq. (4). 8. Fill in the data in Table 3. Table 3. Kinematic viscosity measurement fluid

Temperature (0C)

Tube size

Efflux time (sec)

Viscome ter constant

Kinematic viscosity(cSt)

Kinematic viscosity (m2/s)

Kinematic viscosity from Eq. (4) (m2/s)

Kinematic viscosity from available data (m2/s)

Repeat the absolute viscosity measurement of the selected fluid at several elevated temperatures and fill the data in Table 1.