Question

SI units of coefficient of viscosity are (a) \(\mathrm{kg} \mathrm{s}^{-1} \mathrm{~m}^{-2}\) (b) \(\mathrm{g} \mathrm{m}^{-1} \mathrm{~s}^{-1}\) (c) \(\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}\) (d) \(\mathrm{kg} \mathrm{cm}^{-1} \mathrm{~s}^{-1}\)

Short answer

(c) \( \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1} \)

Step-by-step solution

Understand the Quantity Involved

The coefficient of viscosity, also known as dynamic viscosity, measures a fluid's resistance to flow. It is denoted by \( \eta \). The unit of viscosity is derived from the basic units in the SI system.

Recall the SI Units for Basic Quantities

The SI units for mass, length, and time are \( \text{kilogram} \ (\text{kg}) \), \( \text{meter} \ (\text{m}) \), and \( \text{second} \ (\text{s}) \) respectively.

Determine the Formula for Viscosity

Viscosity \( \eta \) is defined as \( \frac{F}{A} \times \frac{1}{v/l} \) where:- \( F \) is force in newtons (N),- \( A \) is area in square meters (m²),- \( v \) is velocity in meters per second (m/s),- \( l \) is length in meters (m).Rearranging this formula gives \( \eta = \frac{F \cdot l}{A \cdot v} \).

Break Down Force in Terms of SI Units

In the formula \( \eta = \frac{F \cdot l}{A \cdot v} \), force \( F \) is measured in newtons. A newton (N) is defined as \( \text{kg} \cdot \text{m/s}^2 \). Thus, substituting this into the equation, the unit for viscosity becomes \[ \eta = \frac{\text{kg} \cdot \text{m/s}^2 \cdot \text{m}}{\text{m}^2 \cdot \text{m/s}} \].

Simplify the Units

Simplify the expression \( \frac{\text{kg} \cdot \text{m/s}^2 \cdot \text{m}}{\text{m}^2 \cdot \text{m/s}} \):1. Cancel \( \text{m} \) from the numerator with \( \text{m} \) in the denominator (\( \text{m}^2 \)).2. Cancel \( \text{s} \) in \( \text{m/s} \) with \( \text{s} \).This results in \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \).

Choose the Correct Option

Compare the simplified units \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \) with the given options. It matches option (c).

Key concepts

SI Units

SI Units are a set of standards for measurement, which are internationally agreed upon for use in science and technology. Using these units, scientists ensure that their work can be understood and replicated no matter where in the world they are. The core SI units include:

• Meter (m) for length
• Kilogram (kg) for mass
• Second (s) for time
• Ampere (A) for electric current
• Kelvin (K) for temperature
• Mole (mol) for the amount of substance
• Candela (cd) for luminous intensity

In the context of viscosity, we use the units kilogram, meter, and second to derive its SI unit, which is important as it specifies the fluid's resistance to flow under various conditions. Understanding the correct SI unit is critical to accurately measuring and applying this physical property, especially in formulas and practical scenarios.

Fluid Dynamics

Fluid Dynamics is a fundamental part of physics that deals with the motion and behavior of fluids, which include both liquids and gases. When we talk about viscosity in fluid dynamics, we're essentially referring to the internal friction within the fluid that resists flow.
The concept of viscosity is central to many fluid dynamics problems, as it affects how substances move through pipes, how air flows over wings, and even how blood moves through veins. Here are some important aspects:

• High viscosity means a fluid flows more sluggishly, like honey.
• Low viscosity indicates a fluid flows more readily, like water or air.
• Viscosity can depend on temperature, with warmer temperatures often reducing a fluid's viscosity.

Understanding these interactions in fluid dynamics helps engineers design more efficient systems, optimize apparatuses in chemical engineering, and anticipate natural phenomena.

Physics Measurement

In physics, measurement is the cornerstone for understanding and describing the world around us. Viscosity is a perfect example, where precise measurement reveals much about a fluid's flow characteristics. The measurement involves determining how fluids resist motion in response to applied stress.
To measure viscosity accurately:

• Use controlled environments to avoid temperature fluctuations affecting results.
• Instrumentation such as viscometers can provide direct readings of a fluid's viscosity.
• Measurement precision is essential, as slight changes can significantly impact results in scientific and industrial applications.

Accurate physics measurement not only assists in characterizing a material's properties but also provides critical data for designing systems that interact with those materials, leading to more effective and efficient technologies.