Gases are also fluids and share the same physics as liquids. They have:
As the density of the gas decreases, the potential energy between the atoms/molecules which make up the gas also decreases.
An ideal gas has zero potential energy.
There are many devices for measuring pressure.
They all typically use the equation
to relate pressure differences to the height of a column of liquid h of a given density ρ.
The simplest is the manometer.
If P1 > P2 then h > 0
If P1 < P2 then h < 0
Any liquid may be used inside the manometer as long as its density is known.
The most common choice is mercury Hg.
Measuring h and specifying the liquid, allows you to determine the gas pressure being measured.
This leads to another unit of pressure called the torr or mm-Hg.
1 torr = 1 mm-Hg = 133 Pa, 1 atm = 760 torr.
A similar device to a manometer is the barometer.
A tube is filled with a liquid and then inverted with the open end of the tube beneath the surface of a bath of the liquid.
Upon inversion, the fluid in the tube will drop creating a vacuum at the top of the tube.
The height of the column of liquid left in the tube will change with the pressure of the gas upon the bath.
Using
For mercury, a column of height 76 cm can be supported if the gas pressure is 1 atmosphere.
Again, a change in pressure changes the height of the liquid column.
The liquid is not ‘sucked up’ - there is no such thing as a suction force.
The liquid is pushed up by the pressure of the atmosphere.
Since atmospheric pressure decreases with altitude, barometers can be used at altimeters.
In a mercury barometer at atmospheric pressure, the height of the column of mercury in a glass tube is 760 mm. If another mercury barometer is used that has a tube of larger diameter, how high will the column of mercury be in this case?
A small iron ball and a large Styrofoam ball balance in air. If the air is evacuated, the larger ball
A. rises.
==B. falls.==
C. remains in place.
A fluid can be considered to be composed of fluid elements – infinitesimally small fixed amounts (mass) of the fluid with variable volume.
The paths taken by fluid elements are called streamlines.
Fluid flow can be divided into two main types: ==laminar flow and turbulent flow.==
In laminar flow the streamlines do not cross.
In turbulent flow the fluid streamlines do cross.
Fluid kinetic energy is dissipated by viscosity (internal friction).
In laminar flow the dissipation by viscosity is small, in turbulent flow it is large.
When a fluid flows through a pipe the fluid velocity changes with the size of the tube.
The reason is that the mass of the fluid is conserved.
In a given amount of time, the same mass of fluid must pass through every cross-sectional area of the pipe.
At a given location the cross-sectional area of the pipe is A1, the fluid velocity is v1, and its density is ρ1.
In time Δt the mass Δm of fluid which passes through A1 is
At a second location, the cross-sectional area of the pipe is A2, the fluid velocity is v2, and its density ρ_2.
The same amount of fluid must pass through A_2 in time Δt
In order to conserve mass, we require
ρ1 A1 v1=ρ2 A2 v2
This result is called the equation of continuity.
If the fluid densities are the same at the two points (very common for liquids)
As the cross-sectional area of a pipe decreases, the speed of the fluid has to increase.
A fluid can have kinetic and potential energy and the fluid pressure – which is related to a force – can do work.
The kinetic energy of a fluid with density ρ in volume V is
The gravitational potential energy of the fluid is
U_G=m g y=ρV g y
If a fluid expands or contracts it does work
The work done by a fluid with constant pressure P
Consider the fluid flow in a pipe with a variable cross-sectional area. A given fluid element in the pipe will have
Assuming laminar flow, we can equate the mechanical energy of the fluid at one end of the pipe to the mechanical energy at the other, including any work done on or by the fluid.
What we eventually find is
This is known as Bernoulli's equation.
Consider a tank of water with a spigot/tap/faucet.
The fluid density is constant
At both the top of the tank and at the spigot P = P0.
If the tank is very big then v at the top of the tank is ~0.
According to Bernoulli's equation, as the kinetic and potential energies of a fluid increase, the pressure decreases.
Ergo a fast-moving fluid has a lower pressure than a slow-moving fluid (for a fixed y coordinate).
This is called the ==Venturi effect.==
The Venturi effect explains many different phenomena:
Venturi meters are used to measure flow rates through pipes.
In order to remain aloft a plane must generate a 'lift' force to counter its weight.
There are two contributions to the lift:
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