Week 3 Flashcards
What is the primary difference between systems and control volumes?
Systems have a fixed quantity of mass, while control volumes can change as fluids flow through them.
Control volumes are used to analyze fluid motion without tracking individual particles.
How do you calculate the volume flow rate (Q)?
Q is calculated by integrating the velocity component normal to the area over the surface through which the fluid flows.
Q = ∫(Vn dA), where Vn is the component of velocity normal to the area.
What theorem is essential for converting system analysis to control volume analysis?
The Reynolds Transport Theorem.
This theorem applies to all basic physical laws in fluid mechanics.
What does the Reynolds Transport Theorem state?
A system derivative equals the rate of change of B with time within
the control volume plus the flux of B out of the control surface (CS) minus the
flux of B into the control surface
The theorem can be applied to mass, momentum, energy, etc.
When does the Reynolds Transport Theorem change?
The time derivative of the volume integral vanishes for steady flow.
Define incompressible flow.
Incompressible flow assumes negligible density variations in the mass conservation requirement.
Most liquids are treated as incompressible in fluid mechanics.
What are the three basic approaches to analyzing fluid flow problems?
- Control volume analysis
- Differential analysis
- Experimental analysis
These methods allow for different scales and types of fluid mechanics problems to be evaluated.
What is the conservation of mass principle?
The mass of a closed system remains constant over time.
In fluid mechanics, this translates to the mass flow rate in equals the mass flow rate out plus any accumulation.
How is mass flow rate (m) calculated?
Mass flow rate can be calculated by multiplying the volume flow rate (Q) by the fluid density (ρ).
m = Q * ρ.
In the Reynolds Transport Theorem, what does the term ‘B’ represent?
B can represent any property of the fluid, such as mass, energy, or momentum.
The intensive value β = dB/dm represents the amount of B per unit mass.
What is a control volume in fluid mechanics?
A control volume is a specified region in space through which fluid may flow, used for analyzing fluid motion.
It can be fixed, moving, or deformable depending on the analysis.
What is the relationship between inflow and outflow in the conservation of mass for a fixed control volume?
The mass outflow minus the mass inflow plus any accumulation equals the generation of mass in the control volume.
This is often expressed as: Generation = Accumulation + Outflow - Inflow.
True or False: In fluid mechanics, we are generally interested in the path of individual fluid particles.
False.
Fluid mechanics often focuses on the overall flow rather than the path of individual particles.
What is the significance of the component of velocity normal to the area element in control volume analysis?
It determines the direction and rate of flow across the control surface.
This component is crucial for calculating flux through the control surface.
What happens to the time derivative of volume integral in steady flow for a fixed control volume?
It vanishes as long as the intensive property β or density ρ does not vary with time.
This indicates that the system is in a steady state.
What does the term ‘flux terms’ refer to in the context of the Reynolds Transport Theorem?
Flux terms represent the flow of a property (like mass) across the control surface due to inflow and outflow.
They are crucial for calculating changes in the control volume.
What is meant by ‘arbitrarily moving and deformable control volume’?
It refers to a control volume that can change shape and move in an arbitrary manner, complicating the analysis.
These situations require advanced mathematical treatment.
How does the Reynolds Transport Theorem apply to fixed versus moving control volumes?
The conversion formula differs based on whether the control volume is fixed, moving uniformly, or deforming.
Each case requires specific considerations for analyzing fluid properties.
What is the property of all liquids regarding compressibility?
All liquids are nearly incompressible
This implies that density variations are negligible in the mass conservation requirement.
What does the Reynolds transport theorem allow us to do?
Convert system laws to apply to a specific region (control volume)
This can be applied to all the basic laws of Fluid Mechanics.
What is the average velocity in fluid mechanics?
The velocity that, when multiplied by the section area, gives the correct volume flow rate
This definition is crucial for understanding flow rates in fluid systems.
What is the formula for volume flow passing through a given cross section?
Qi = Vi Ai
Here, Qi is the volume flow, Vi is the average velocity, and Ai is the cross-sectional area.
What is the significance of a control volume in Fluid Mechanics?
It allows for the application of system laws to a specific region occupied by the system
Control volumes can be analyzed for only an instant.
What does the term ‘inlets and outlets are one-dimensional’ refer to?
Flow conditions where the flow can be analyzed in 1D
This simplifies the calculations in fluid flow analysis.
