Question

The upper limit of the scale of dial reading for a rotational oilfield viscometer is 300 degrees. At a rotational speed of 100 RPM, the highest possible effective (apparent) viscosity that can be measured on this viscometer (in cP) is ________ (rounded off to one decimal place).
[Given: 1 degree dial reading = 5.11 dynes/cm2, and 1 RPM = 1.703 s^-1]

Hint:

Convert the maximum dial reading to shear stress and the RPM to shear rate, then divide the two to get the apparent viscosity.

Answer 1

Correct Answer: 900.2

Step 1: List the given data:
Maximum dial reading = 300 degrees
Rotational speed N = 100 RPM
1 degree dial reading = 5.11 dynes/cm2
1 RPM = 1.703 s^-1
Step 2: Convert the maximum dial reading into shear stress:
Shear stress tau = 300 x 5.11
tau = 1533 dynes/cm2
Step 3: Convert this shear stress into SI units (Pa), using 1 dyne/cm2 = 0.1 Pa:
tau = 1533 x 0.1
tau = 153.3 Pa
Step 4: Convert the rotational speed into shear rate:
Shear rate = 100 x 1.703
Shear rate = 170.3 s^-1
Step 5: Compute the effective (apparent) Newtonian viscosity from the ratio of shear stress to shear rate:
\[ \mu_a = \frac{\tau}{\dot{\gamma}} = \frac{153.3}{170.3} \]
mu_a = 0.90018 Pa.s
Step 6: Convert this viscosity from Pa.s into centipoise, using 1 Pa.s = 1000 cP:
mu_a = 0.90018 x 1000
mu_a = 900.2 cP
Final Answer:
\[ \boxed{\mu_a = 900.2 \text{ cP}} \]