Pressure in gases
In the following, a thin metal can has a little water put in it. With the lid off, the water is bought to the boil, and boiled for a short time.
The heat is turned off, and the lid quickly secured. After a while the can collapses.
This is because:
A tube, sealed at one end, about 1m long, is filled with mercury (‘Hg’) and its open end is placed under mercury in a dish. It is then raised to the vertical. A gap appears in the tube – and this must be a vacuum since no air has been able to enter.
It is the vertical height that matters – no gap appears until it is more than about 76cm.
The only thing that can be holding the column of mercury up is the air pressure acting on the mercury in the dish.
This arrangement can be used as a simple barometer (a device for measuring air pressure) since, as the air pressure varies a little daily, the height of the Hg column also varies.
Pressure in liquids
The holes are at the same level and water shoots out equal distances from each.
This indicates that:
This indicates that:
It can be shown that the pressure below the surface of a fluid is given by:
The height h represents the ‘excess’ pressure of the gas – the amount by which it is greater than atmospheric pressure.
Liquids in a U-tube
If two immiscible liquids (i.e. which do not mix, such as oil and water) are put in a u-tube, they will settle to different levels, unless they have the same density:
The pressure at the same horizontal level is the same, so:
A block of steel cannot float, because steel is denser than water, and so the block does not displace enough water to equal its own weight. However, when steel is formed into the shape of a boat, it can displace enough water to enable it to float.
A cork needs only displace a small amount of water to balance its own weight, so it sits high in the water.
Hot air balloons also make use of Archimedes’ principle.
The forces on the opposite vertical sides of the object balance each other.
But the force up is greater than the force down, since pressure increases with depth, and the difference between them equals the upthrust.
FLUIDS IN MOTION (return to start of page)
Consider a liquid flowing slowly through a pipe:
Fluid molecules (liquid and gas molecules) tend to stick to solid surfaces. In the above set-up, the molecules immediately next to the pipe are at rest. But towards the centre they get faster. This is indicated by the arrows, representing velocity, getting longer towards the middle.
This also occurs in rivers. The water flows faster in the middle than near the banks, and faster at the top than near the bottom.
Since layers of molecules immediately next to each other are moving at different speeds, they must be sliding over each other. This relative motion is opposed by forces between the molecules, i.e. there is fluid friction. The situation is similar to dragging a block of wood across a bench - there is friction between the wood and the bench producing a resistive force.
The viscosity of a fluid influences:
A section of pipe carrying a moving fluid:
Poiseuille showed that for steady flow, if volume V passed a fixed point in time t, then the volume flow rate (V/t) is given by:
Expression for mass flow rate:
V = the rate of flow of a liquid along a pipe
V/ = the rate of flow when the length is doubled, the radius is halved, the pressure difference between the ends is doubled, the viscosity is halved. What is V/ in terms of V?
Streamline and turbulent flow
The following indicates how the paths of water flowing along a pipe can be made visible. The coloured liquid is released slowly through a small hole, and it follows a streamline in the water.
There are two types of fluid flow:
The resistance of a fluid to flow increases a lot when the flow becomes turbulent. This applies not just to a fluid flowing through a pipe, but when an object moves through a fluid. This is an important consideration in the design of cars etc.
The equation of continuity
Consider a fluid undergoing streamline flow though a pipe whose cross-sectional area decreases.
Setting these masses equal to each other:
Thus, the equation of continuity says that the mass per second passing all points in a pipe is the same.
Now, a liquid (unlike a gas) is almost incompressible, i.e. it
has a constant density.
Thus, for a liquid, the above equations reduce to:
Unit of Av = m2 m s-1 = m3 s-1º volume per second (or, volume flow rate)
So, for a liquid, the equation of continuity says that the volume per second passing all points in a pipe is the same.
This implies that the smaller the area A, the bigger the velocity v (imagine ‘nipping’ the end of a hose pipe - the area gets smaller and the water shoots out quicker)
What is the velocity of the emerging spray?
The Bernoulli effect
The top moves down if you blow into the tunnel. This is because the moving air inside has a lower pressure than the still air outside, and so the extra pressure on the top outside pushes the top down.
c) The Venturi meter
The above type of arrangement can be inserted into a pipe carrying a liquid, and the flow rate can be determined from the height difference, h.
The top part of the aerofoil is made longer than the bottom part:
As the aerofoil moves through the air, the air has to move further over the top than the bottom, and so has to move faster to ‘keep up’, and so has less pressure. The pressure on the bottom is therefore greater than that on the top, hence a net upward force, called ‘lift’, occurs.
An aeroplane flying horizontally at a constant speed has four basic forces acting on it, which are balanced in pairs:
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A Level Physics - Copyright © A
C Haynes 1999 & 2004