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Chapter 11: Problem 1

Distinguish between flow of an ideal gas and inviscid flow of a fluid.

Short Answer

Expert verified
Ideal gas flow, governed by the ideal gas law, considers particles with no interaction except during elastic collisions, and the flow can change due to variations in temperature, pressure, and volume. Inviscid fluid flow refers to a zero-viscosity fluid with no internal frictional forces between different fluid layers, governed by Euler's equations. Its flow is not affected by shear stress or friction.

Step by step solution

01

Define Ideal Gas

An ideal gas is a theoretical gas composed of particles on a lattice site, with no interaction except for completely elastic collision. The ideal gas law governs its behavior, PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
02

Define Inviscid Flow

Inviscid flow refers to the flow of a fluid with zero viscosity. In other words, there are no internal frictional forces between different layers of the fluid while it's in motion. This is also a theoretical concept, as all real fluids have some viscosity. The Euler's equations govern the flow of inviscid fluids.
03

Compare

The flow of an ideal gas can change due to variations in temperature, pressure, and volume, while the inviscid fluid flow is not affected by any shear stress or friction due to its zero viscosity nature. Ideal gas molecules are considered to have no size and do not interact with each other except during elastic collisions, while inviscid fluid flow does not consider the interaction forces between liquid molecules.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ideal Gas
An ideal gas is a theoretical construct that simplifies the behavior of gases by assuming a set of specific conditions. Imagine gas particles as tiny, infinitely small spheres bouncing around in space. These spheres are ideal in the sense that:
  • They only undergo elastic collisions, meaning that they do not stick together or experience any attraction or repulsion.
  • They are in constant random motion.
  • Their collisions with the walls of their container create the pressure we measure.
These assumptions make it easier to describe the gas using the Ideal Gas Law, a straightforward mathematical equation that models this behavior under a variety of conditions. Despite being an approximation, the ideal gas model is quite useful and provides a foundation for understanding more complex behaviors in gases.
Inviscid Flow
Inviscid flow describes the movement of a fluid that is assumed to have no viscosity. Viscosity is a measure of a fluid's resistance to shear or flow. So, in an inviscid flow scenario, it is as if the fluid can move without any internal friction or resistance between its particles. This type of flow is often utilized in fluid dynamics to simplify calculations because:
  • It eliminates the complex mathematical treatment required to handle viscous forces.
  • It allows focus solely on pressure and inertial forces affecting the fluid.
While perfectly inviscid fluids do not exist in the real world, this theoretical concept is especially useful in understanding certain fluid flow phenomena and is integral in studying aerodynamics and fluid mechanics at high velocities or low-viscosity conditions.
Euler's Equations
Euler's Equations are fundamental equations in fluid dynamics describing the motion of an inviscid fluid. Named after the Swiss mathematician Leonhard Euler, these equations help understand how such a fluid evolves over time and space without considering viscosity. The equations consist of:
  • Conservation of Mass (Continuity Equation)
  • Conservation of Momentum
  • Conservation of Energy
Euler鈥檚 equations are presented mathematically as a set of partial differential equations. They analyze the fluid flow based on pressure effects and changes in fluid velocity, making them essential in contexts where viscous effects are negligible. This makes them pivotal in fields like astrophysics and aerodynamics, helping predict the movement and stability of different fluid systems.
Ideal Gas Law
The Ideal Gas Law is a cornerstone of classical thermodynamics that simplifies and unifies the behaviors of gases under various conditions. Expressed as \( PV = nRT \), this formula relates four key variables:
  • **P** - Pressure of the gas
  • **V** - Volume occupied by the gas
  • **n** - Number of moles of the gas
  • **R** - Ideal gas constant, a universal constant
  • **T** - Absolute temperature
This equation provides invaluable insights by predicting how a gas will behave as any of these variables change. Though it's based on an idealized model, the Ideal Gas Law enables scientists and engineers to model and anticipate gas behaviors with impressive accuracy in many real-world situations, like in chemistry labs and industrial processes involving gas reactions and transformations.

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Most popular questions from this chapter

At a certain point in a pipe, air flows steadily with a velocity of \(150 \mathrm{m} / \mathrm{s}\) and has a static pressure of \(70 \mathrm{kPa}\) and a static temperature of \(4^{\circ} \mathrm{C}\). The flow is adiabatic and frictionless.

An air heater in a large coal-fired steam generator heats fresh air entering the steam generator by cooling flue gas leaving the steam generator. One million lbm/hr of air at \(100^{\circ} \mathrm{F}\) and 1.1 million lbm/hr of flue gas at \(720^{\circ} \mathrm{F}\) enters the air heater. The flue gas leaves at \(310^{\circ} \mathrm{F}\). Flue gas has \(c_{p}=0.26 \mathrm{Btu} / \mathrm{lbm}^{\circ} \mathrm{F}\) and \(k=1.39 .\) Pressure changes are small and may be neglected. Calculate the temperature of the air leaving the air heater and the total entropy change for the process.

Air enters a frictionless, constant area duct with \(\mathrm{Ma}=2.5\) \(T_{0}=20^{\circ} \mathrm{C},\) and \(p_{0}=101 \mathrm{kPa}(\mathrm{abs}) .\) The gas is decelerated by heating until a normal shock occurs where the local Mach number is \(1.3 .\) Downstream of the shock, the subsonic fow is accelerated with heating until it exits with a Mach number of \(0.9 .\) Determine the static temperature and pressure, the stagnation temperature and pressure, and the fluid velocity at the duct entrance, just upstream and downstream of the normal shock, and at the duct exit. Sketch the temperature- entropy diagram for this flow.

Supersonic airflow enters an adiabatic, constant area (inside diameter \(=1 \mathrm{ft}\) ) 30 -ft-long pipe with \(\mathrm{Ma}_{1}=3.0 .\) The pipe friction factor is estimated to be \(0.02 .\) What ratio of pipe exit pressure to pipe inlet stagnation pressure would result in a normal shock wave standing at (a) \(x=5\) ft, or \((\mathbf{b}) x=10 \mathrm{ft},\) where \(x\) is the distance downstream from the pipe entrance? Determine also the duct exit Mach number and sketch the temperature-entropy diagram for each situation.

An ideal gas flows isentropically through a convergingdiverging nozzle. At a section in the converging portion of the nozzle. \(A_{1}=0.1 \mathrm{m}^{2}, p_{1}=600 \mathrm{kPa}(\mathrm{abs}), T_{1}=20^{\circ} \mathrm{C},\) and \(\mathrm{M} \varepsilon_{1}=0.6 .\) For section (2) in the diverging part of the nozzle, determine \(A_{2}, p_{2},\) and \(T_{2}\) if \(\mathrm{Ma}_{2}=3.0\) and the gas is air.
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