Examples of Ideal Fluid in the following topics:
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- For an ideal fluid we found that the stress tensor took a particular form,
- where $w=(\epsilon + P)/\rho$ is the heat function (enthalpy) per unit mass of the fluid.
- In the ideal fluid, no heat is transferred between different parts of the fluid, so if we denote $s$ as the entropy per unit rest mass we have
- for a bunch of fluid; therefore, we also have a continuity equation for the entropy
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- Torricelli's law is theorem about the relation between the exit velocity of a fluid from a hole in a reservoir to the height of fluid above the hole.
- Torricelli's law is theorem in fluid dynamics about the relation between the exit velocity of a fluid from a sharp-edged hole in a reservoir to the height of the fluid above that exit hole .
- This relationship applies for an "ideal" fluid (inviscid and incompressible) and results from an exchange of potential energy,
- Due to the assumption of an ideal fluid, all forces acting on the fluid are conservative and thus there is an exchange between potential and kinetic energy.
- The exit velocity depends on the height of the fluid above the exit hole.
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- For "ideal" flow along a streamline with no change in height, an increase in velocity results from a decrease in static pressure.
- The relationship between pressure and velocity in ideal fluids is described quantitatively by Bernoulli's equation, named after its discoverer, the Swiss scientist Daniel Bernoulli (1700–1782).
- Bernoulli's equation states that for an incompressible and inviscid fluid, the total mechanical energy of the fluid is constant .
- (An inviscid fluid is assumed to be an ideal fluid with no viscosity. )
- Syphoning fluid between two reservoirs.
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- A fluid is a substance that continually deforms (flows) under an applied shear stress.
- The distinction between solids and fluid is not entirely obvious.
- It is best described as a viscoelastic fluid.
- This also means that all fluids have the property of fluidity.
- In contrast, ideal fluids can only be subjected to normal, compressive stress (called pressure).
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- If we assume that ${\bf F}/m = -\nabla \phi$ which is often the case, we find that if the flow in an isentropic, ideal fluid is initially irrotational it will remain irrotational.
- taken along some closed contour that moves with the fluid.
- Because $\delta {\bf r}$ is the difference between two positions moving with the fluid we have
- if $\displaystyle {\bf F}/m = -\nabla \phi$, so the circulation around a contour moving with the fluid is constant if the flow is isentropic.
- The circulation around a close contour (bold lines) that travels with the fluid along the streamlines (light lines) is conserved if the fluid is isentropic.
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- Let's imagine a different type of wave on a fluid.
- Let's imagine we have two fluids in a gravitational field.
- The lower fluid has density $\rho'$, velocity $U'$ and thickness $h'$ and the upper fluid has density $\rho$, velocity $U$ and thickness $h$.
- To examine the pressure let's take Euler's equation for the ideal fluid and substitute ${\bf V}=-\nabla \Phi$ to yield
- The gravitational acceleration $g$ can be due to gravity (as in a supernova) or due to a deceleration of the fluid, if a low-density fluid plows into a high-density fluid.
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- Discontinuities signal a failure of fluid mechanics as we have formulated it.
- Let $P_1, \rho_1$ and $v_1$ denote the physical quantities on the left-hand side (the pre-shock fluid) and $P_2, \rho_2$ and $v_2$ in the post-shock fluid.
- If you remember the energy flux for an ideal fluid is
- The post-shock fluid has higher pressure and density.
- Let's specialize for an ideal gas, for which $w = \gamma/(\gamma - 1) p V$, so
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- Barometers are devices used for measuring atmospheric and gauge pressure indirectly through the use of hydrostatic fluids.
- However, it is important to determine whether it is necessary to use absolute (gauge plus atmospheric) pressure for calculations, as is often the case for most calculations, such as those involving the ideal gas law.
- Early barometers were used to measure atmospheric pressure through the use of hydrostatic fluids.
- The density of the liquid is p, g is the acceleration due to gravity, and h is the height of the fluid in the barometer column.
- The concept of determining pressure using the fluid height in a hydrostatic column barometer
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- Pressure is an important physical quantity—it plays an essential role in topics ranging from thermodynamics to solid and fluid mechanics.
- The pressure exerted by an ideal gas on a closed container in which it is confined is best analyzed on a molecular level.
- For such an ideal gas confined within a rigid container, the pressure exerted by the gas molecules can be calculated using the ideal gas law:
- where n is the number of gas molecules, R is the ideal gas constant (R = 8.314 J mol-1 K-1), T is the temperature of the gas, and V is the volume of the container.
- This image is a representation of the ideal gas law, as well as the effect of varying the equation parameters on the gas pressure.
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- Atmospheric pressure is the magnitude of pressure in a system due to the atmosphere, such as the pressure exerted by air molecules (a static fluid) on the surface of the earth at a given elevation.
- For most working fluids where a fluid exists in a closed system, gauge pressure measurement prevails.
- While gauge pressure is very useful in practical pressure measurements, most calculations involving pressure, such as the ideal gas law, require pressure values in terms of absolute pressures and thus require gauge pressures to be converted to absolute pressures.