Question

Which physical quantity has unit of pascal - second? (a) Velocity (b) viscosity (c) energy (d) coefficient of viscosity

Short answer

The physical quantities that have the unit of Pascal-second (Pa·s) are (b) viscosity and (d) coefficient of viscosity.

Step-by-step solution

Understanding Units

The units of given options are: (a) Velocity - meters per second (m/s) (b) Viscosity - Pascal-second (Pa·s) (c) Energy - Joule (J) (d) Coefficient of Viscosity - Pascal-second (Pa·s)

Comparing Units

Now, we compare the units of the given options with Pascal seconds. (a) Velocity: meter per second (m/s) is not equal to Pascal-second (Pa·s). (b) Viscosity: Pascal-second (Pa·s) is equal to Pascal-second (Pa·s). (c) Energy: Joule (J) is not equal to Pascal-second (Pa·s). (d) Coefficient of Viscosity: Pascal-second (Pa·s) is equal to Pascal-second (Pa·s). So, both options (b) Viscosity and (d) Coefficient of Viscosity have the unit Pascal-second (Pa·s).

Key concepts

Viscosity

Viscosity is a fundamental concept in fluid dynamics. It describes a fluid's resistance to flow. Imagine honey and water: honey flows more slowly than water. This is because honey has a higher viscosity. Viscosity is important in understanding how fluids move.
For example, engineers need to know the viscosity of oil to design effective machinery. In biological systems, viscosity affects how blood flows through the vessels. Essentially, viscosity can change how we design anything involving fluids like pipes and aerodynamics.
In simple terms, viscosity is like the 'thickness' of a fluid.

• High viscosity: Sticky or thick (like honey)
• Low viscosity: Runny or thin (like water)

Coefficient of Viscosity

The coefficient of viscosity provides a specific measure of a fluid's resistance to shear or flow. It is a more precise way to quantify viscosity. The term 'coefficient' here suggests it is a proportionality factor in a formula.
This coefficient is crucial in equations governing the flow of fluids, such as Poiseuille's Law, which calculates the flow rate of liquid through a pipe. In mathematical terms, the coefficient of viscosity is used in equations like:\[\tau = \, \eta \, \cdot \, \left( \frac{du}{dy} \right)\]Where \( \tau \) is the shear stress, \( \eta \) is the coefficient of viscosity, and \( \frac{du}{dy} \) is the velocity gradient perpendicular to the flow direction.
Knowing the coefficient of viscosity helps in many engineering applications, from designing car engines to understanding natural processes like lava flow in volcanoes.

Units of Measurement

Units of measurement standardize our understanding of physical quantities. For viscosity, the unit is the Pascal-second (Pa·s). This unit combines force (in Pascals) and time (in seconds), offering a clear impression of how force is related to straining a fluid.
In the International System of Units (SI), almost every physical quantity has a specific unit. For speed, we use meters per second (m/s), for mass, kilograms (kg), and for energy, Joules (J).
Understanding these units allows scientists and engineers to communicate effectively and ensure accuracy in their work.

• Velocity: measured in meters per second (m/s)
• Viscosity & Coefficient of Viscosity: both measured in Pascal-second (Pa·s)
• Energy: measured in Joules (J)

The Pascal-second is an example of how units convey specific information about the properties of fluids, allowing us to design, understand, and predict their behavior.