Conceptual questions in Fluid Mechanics

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SUMMARY

This discussion focuses on key concepts in Fluid Mechanics, specifically defining static pressure, dynamic pressure, the continuum hypothesis, kinetic viscosity, and kinematic viscosity. Static pressure is the pressure exerted by a fluid on an object, while dynamic pressure is calculated using the formula q = 1/2 ρv². The continuum hypothesis involves subdividing a region into infinitesimal volume elements that are uniform and statistically significant. Kinetic viscosity is often confused with dynamic viscosity, which measures a fluid's internal resistance to flow, while kinematic viscosity is the ratio of dynamic viscosity to fluid density. The discussion highlights the importance of understanding these definitions for practical applications in fluid systems.

PREREQUISITES
  • Understanding of Fluid Mechanics principles
  • Familiarity with pressure concepts in fluid systems
  • Knowledge of viscosity types: dynamic and kinematic
  • Basic mathematical skills for fluid dynamics equations
NEXT STEPS
  • Research the implications of the continuum hypothesis in fluid dynamics
  • Study the differences between dynamic and kinematic viscosity in detail
  • Explore pressure gradients in various fluid systems, particularly in PWRs (Pressurized Water Reactors)
  • Learn about the practical applications of viscosity measurements in engineering
USEFUL FOR

Students and professionals in engineering, particularly those specializing in fluid mechanics, mechanical engineering, and chemical engineering, will benefit from this discussion. It provides foundational knowledge essential for understanding fluid behavior in various applications.

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Homework Statement


Define:Static pressure
Dynamic Pressure
Continuum hypothesis
Kinetic Viscosity
Kinematic Viscosity

2. The attempt at a solution

The real question is : are these answers sufficient?

Static Pressure
- The pressure exerted by a fluid on an object placed within the fluid is called the static pressure.

Dynamic Pressure - The pressure exerted by a fluid on an object that is moving through the fluid. This is given by:
q = \frac{1}{2} \rho v^2

I get the feeling that this is wrong...

Continuum hypothesis - the region to be described can be subdivided into a set of (infinitesimal) volume elements, each of which simultaneously:
1) is small enough to be considered uniform (i.e. any spatial variations in properties -- such as r, v,T, p -- inside the volume element are negligible); and
2) is large enough to contain a statistically large number of molecules.

Kinetic Viscosity - I think he means dynamic viscosity
The definition for dynamic viscosity is the force per unit area a liquid exerts on two parallel plates that enclose the liquid. I would be more concise with this explanation when I'm writing it out that is, i will give an example.

Kinematic Viscosity - The ratio of the dynamic viscosity and the density of the fluid.

I am not sure about the last two definitions, i think they are too short. However i have looked through a few textbooks - Lifsitz/Landau, Houghton/Carpenter (my course text), Batchelor, but none of them have yielded a satisfactory answer for the last two definitions.
I would really appreciate your help!

Thank you
 
Physics news on Phys.org
I like these definitions:
Dynamic viscosity (also known as absolute viscosity) is the measurement of the fluid’s internal resistance to flow while kinematic viscosity refers to the ratio of dynamic viscosity to density. Based on the expression above, two fluids with the same dynamic viscosities can have very different kinematic viscosities depending on density and vice versa. As a result, grasping the physical meaning of these two material properties may not always be so easy.
Simply put, dynamic viscosity gives you information on the force needed to make the fluid flow at a certain rate, while kinematic viscosity tells how fast the fluid is moving when a certain force is applied.

Ref: https://blog.rheosense.com/what-are-the-differences-between-dynamic-and-kinematic-viscosities

A similar discussion - https://www.machinerylubrication.com/Read/31591/dynamic-kinematic-viscosity
Kinematic viscosity incorporates fluid density as part of its measurement. Thus, dynamic viscosity is a measure of force, while kinematic viscosity is a measure of velocity. That's the difference. If you divide kinematic viscosity by the fluid density, you get absolute viscosity.

As for dynamic and static pressure, consider in a PWR, there is a pressure gradient around the fluid circuit. The highest pressure is found at the outlet of the pump, while the lowest pressure is found at the inlet of the pump. The pump adds energy and momentum to the flow.

The pressurizer adds a 'static' pressure to the system. The pressurizer, located on one of the hot legs simply maintains a head of water and pressure from steam above the water. When one sees a nominal system pressure (~ 2250 psia or ~155 bar (depending on plant), that usually refers to the pressure in the pressurizer. The core has a pressure drop of something like 25 psid (1.73 bar) and the pressure vessel a pressure drop (including core) of something like 40 psid (2.76 bar), there are additional pressure drops in the downcomer, piping (cold leg) between pump and downcomer, piping (hot leg) from pressure vessel to steam generator, the steam generator itself, and the piping from steam generator back to the pump.
 
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