Dynamic viscosity μ of a fluid is

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Question restatement: Dynamic viscosity μ of a fluid is

Answer options presented:
- a. a function of temperature.
- b. a function of flow velocity.
- c. a function of density.
- d. a function of pressure.
- e. a function of surface tension.

Analysis of each option:

Option a: a function of temperature.
- For most fluids, especially liquids, dynamic viscosity varies with temperature: as temperature increases, intermolecular interactions change and viscosity typically decreases. This dependence is a fundamental characteristic used in many practical calculations (e.g., viscosity charts, Arrhenius-type relations). Therefore, this statement is true.

Option b: a function of flow velocity.
- In Newtonian fluids, dynamic viscosity μ is a material property that does not depend on the flow velocity or shear rate. The shear stress is proportional to shear rate with μ as the constant of proportionality. However, for non-Newtonian fluids, apparent viscosity can depend on shear rate, surface conditions, or history. Since the question specifies dynamic viscosity μ (a standard property), this option is generally false in the Newtonian context. It can be true only for certain non-Newtonian fluids in specific regimes, which makes it unreliable as a general statement.

Option c: a function of density.
- Dynamic viscosity is not determined by density; while both can vary with temperature or pressure, μ itself is not a direct function of density. This option is incorrect.

Option d: a function of pressure.
- For liquids, viscosity changes with pressure only very slightly; for gases, viscosity increases with pressure more noticeably but is often described as primarily temperature-dependent with pressure effects being secondary or included via more complex models. The standard, broadly taught statement is that μ is a function of temperature, and in gases, also a function of temperature (and to a lesser extent, pressure). Given the common interpretation and the provided answer set, this option is treated as true in contexts where pressure dependence is acknowledged (noting that the dependence is generally weaker than the temperature dependence for liquids).

Option e: a function of surface tension.
- Surface tension is a separate property related to the interface between phases and does not determine dynamic viscosity. This option is incorrect.

Summary of reasoning flow: The core concept is that dynamic viscosity μ is primarily a material property linked to temperature (for both liquids and gases) and, in gases, can show some pressure dependence, whereas dependencies on flow velocity, density, or surface tension do not define μ in the standard sense. The statements about velocity and density misinterpret μ as a variable property tied to those factors, which is not generally true. The statement about surface tension confuses two different interfacial properties.

BH40A1401 Fluid Mechanics I - Contact teaching, Lappeenranta 6.1.2025-23.2.2025 Homework 1

Dynamic viscosity μ of a fluid is

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