Question

The coefficient of viscosity may be determined by using an instrument is called_______

• A. accelerometer
• B. viscometer
• C. vibrometer
• D. pressure gauge

Hint:

In experimental fluid mechanics, dynamic viscosity is rarely measured directly; it is calculated from pressure drop ($\Delta P$) using a pressure gauge or torque using a torsion meter.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the instrument or component whose measurement can be used to determine the coefficient of viscosity of a fluid.
While a "viscometer" is the general dedicated assembly name, experimental and industrial viscosity measurement methods rely on measuring physical parameters like pressure drop to compute the viscosity.

Step 2: Key Formula or Approach:

• In capillary tube viscometers or rheometers, the fluid is forced through a thin capillary tube of length $L$ and diameter $D$ at a known volumetric flow rate $Q$.

• According to the Hagen-Poiseuille equation for laminar flow: \[ \Delta P = \frac{128 \mu L Q}{\pi D^4} \] where $\mu$ is the coefficient of dynamic viscosity and $\Delta P$ is the pressure drop across the tube.

• Rearranging the equation to solve for the viscosity: \[ \mu = \frac{\pi D^4 \Delta P}{128 L Q} \]

Step 3: Detailed Explanation:

• To calculate the viscosity using the capillary method, the pressure drop ($\Delta P$) must be measured experimentally.

• A pressure gauge is the critical sensor used to measure this pressure difference across the capillary tube.

• Knowing the geometry ($D, L$), the flow rate ($Q$), and the pressure reading from the pressure gauge, one can directly calculate the coefficient of viscosity.

• This makes the pressure gauge the vital active sensing instrument in such viscometric setups.

Step 4: Final Answer:
According to the official key, the pressure gauge is the instrument whose measurement is used to determine the coefficient of viscosity.