Measurement of Small Pressure Differences

Measurement of Small Pressure Differences

Accurate measurement of small differences of air pressure is often
required in experimental aerodynamics. A convenient instrument
is the Chattock gauge (Fig. 4). The rigid glasswork AB forms a
U-tube, and up to the levels L contains water, which also fills the
central tube T. But above L and the open mouth of T the closed
vessel surrounding this tube is filled with castor oil. Excess of air
pressure in A above that in B tends to transfer water from A to B
by bubbling through the castor oil. But this is prevented by tilting
the heavy frame F, carrying the U-tube, about its pivots P by means
of the micrometer screw S, the water-oil meniscus M being observed
for accuracy through a microscope attached to F. Thus the excess
air pressure in A is compensated by raising the water level in B
above that in A, although no fluid passes. The wheel W fixed to S
is graduated, and a pressure difference of O0005 in. of water is easily

FIG. 4. CHATTOCK GAUGE.

detected. By employing wide and accurately made bulbs set close

together, constantly removing slight wear, protecting the liquids

against appreciable temperature changes and plotting the zero

against time to allow for those that remain, the sensitivity

* may be

increased five or ten times. These gauges are usually constructed

for a maximum pressure head of about 1 in. of water. Longer forms

extend this range, but other types are used for considerably greater

heads.

At 15 C. 1 cu. ft. of water weighs 62-37 Ib. Saturation with air

decreases this weight by about 0'05 Ib. The decrease of density

from 10 to 20 C. is 0-15 per cent. A 6 or 7 pet cent, saline solution

is commonly used instead of pure water in Chattock gauges, however,

since the meniscus then remains clean for a longer period.

The Hydrostatic Equation

The Hydrostatic Equation

We now approach the problem of the equilibrium of a bulk of air
at rest under the external force of gravity, g has the dimensions of
an acceleration, L/T*. Its value depends slightly on latitude and
altitude, increasing by 0-5 per cent, from the equator to the poles
and decreasing by 0-5 per cent, from sea-level to 10 miles altitude,
At sea-level and 45 latitude its value is 32173
in ft.-sec. units. The value 32-2 ft./sec.

2 is sufficiently accurate for most purposes.
Since no horizontal component of external force
acts anywhere on the bulk of air, the pressure
in every horizontal plane is constant, as otherwise
motion would ensue. Let h represent altitude, so
that it increases upward. Consider an elementcylinder
of the fluid with axis vertical, of length
SA and cross-sectional area A .

Pressure

Pressure

Consider a small rigid surface suspended in a bulk of air at rest.
The molecular motion causes molecules continually to strike, or
tend to strike, the immersed surface, so that a rate of change of
molecular momentum occurs there. This cannot have a component
parallel to the surface, or the condition of rest would be disturbed.
Thus, when the gas is apparently at rest, the aggregate rate of
change of momentum is normal to the surface ; it can be
represented by a force which is everywhere directed at right
angles towards the surface. The intensity of the force per unit
area is the pressure pt sometimes called the hydrostatic or static
pressure.

It is important to note that the lack of a tangential component to
p depends upon the condition of stationary equilibrium. The
converse statement, that fluids at rest cannot withstand a tangential
or shearing force, however small, serves to distinguish liquids from
solids. For gases we must add that a given quantity can expand to
fill a volume, however great.

It will now be shown that the pressure at a point in a fluid at rest is
uniform in all directions. Draw the small tetrahedron ABCO, of

* In this system, the units of length and time are the foot and the second, whilst
forces are in pounds weight. It is usual in Engineering, however, to omit the word ' weight/ writing

*Ib.' for 'lb.-wt.,' and this convention is followed. The
appropriate unit of mass is the 'slug,' viz. the mass of a body weighing g Ib.
Velocities are consistently measured in ft. per sec., and so on. This system being
understood, specification of units will often be omitted from calculations for brevity.
For example, when a particular value of the kinematic viscosity is given as a number,
sq. ft. per sec. will be implied. It will be desirable occasionally to introduce special
units. Thus the size and speed of aircraft are more easily visualised when weights
are expressed in tons and velocities in miles per hour. The special units will be
duly indicated in such cases. Non-dimeasional coefficients are employed wherever
convenient.

Density

Density

Air is thus not a continuum. If it were, the density at a point would be defined as follows : considering the mass M of a small volume V of air surrounding the point, the density would be
the limiting ratio of M/V as V vanishes. But we must suppose that the volume V enclosing the point is contracted only until it is small compared with the scale of variation of density, while it still remains large compared with the mean distance separating the molecules. Clearly,however, V can become very small before the continuous passage of molecules in all directions across its bounding surface can make indefinite the number of molecules enclosed and M or M/V uncertain. Density is thus defined as the ratio of the mass of this very small, though finite, volume of air i.e. of the aggregate mass of the molecules enclosed to the volume itself. Density is denoted by p, and has the dimensions M/Z.

In Aerodynamics it is convenient to use the slug-ft.-sec. system of units.* At 15 C. and standard pressure 1 cu. ft. of dry air weighs 0-0765 Ib. This gives p = 0-0765/g = 0-00238 slug per cu. ft.
It will be necessary to consider in many connections lengths, areas, and volumes that ultimately become very small. We shall tacitly assume a restriction to be imposed on such contraction as discussed above. To take a further example, when physical properties are attached to a '
point' we shall have in mind a sphere of very small but sufficient radius centred at the geometrical point.

AIR AT REST, THE ATMOSPHERE AND STATIC LIFT

AIR AT REST, THE ATMOSPHERE AND STATIC LIFT


Air at sea-level consists by volume of 78 per cent, nitrogen, 21 per cent, oxygen, and nearly 1 per cent, argon, together with traces of neon, helium, possibly hydrogen, and other gases.

Although the constituent gases are of different densities, the mixture is maintained practically constant up to altitudes of about 7 miles in temperate latitudes by circulation due to winds. This lower part of the atmosphere, varying in thickness from 4 miles at the poles to 9 miles at the equator, is known as the troposphere. Above it is the stratosphere, a layer where the heavier gases tend to be left at lower levels until, at great altitudes, such as 50 miles, little but helium or
hydrogen remains. Atmospheric air contains water-vapour in varying proportion, sometimes exceeding 1 per cent, by weight. 

From the point of view of kinetic theory, air at a temperature of C. and at standard barometric pressure (760 mm. of mercury) may be regarded statistically as composed of discrete molecules, of mean diameter 1-5 X 10 ~ 5 mil (one-thousandth inch), to the number of 4-4 x 1011 per cu. mil. These molecules are moving rectilinearly in all directions with a mean velocity of 1470 ft. per sec., i.e. onethird faster than sound in air. They come continually into collision with one another, the length of the mean free path being 0-0023 mil.

Helicopter Fuel Systems

Helicopter Fuel Systems

Figure 1.7 illustrates a typical fuel system found in a light turbine powered helicopter. This system incorporates, a single bladder type fuel cell, located below and aft of the rear passenger seat. Installed in the fuel cell are two submersible centrifugal-type boost pumps, an upper and lower fuel quantity indicating probe, and a solenoid operated sump drain.

The boost pumps are connected so that their outlet ports join to form a single line to the engine. Either pump is capable of supplying sufficient fuel to operate the engine. Check valves are installed at the outlet of each pump, and a pressure switch located in the outlet port of each pump will il­luminate the FUEL BOOST CAUTION LIGHT in case of a pump failure.

An electrically operated shut-off valve is in­stalled in the fuel line running from the tank to the engine. A fuel selector valve is not necessary be­cause only one tank is used in this system.

Fuel is filtered twice before entering the engine, and each filter is equipped with a warⁿing light to indicate filter^- clogging. Additional provisions are made in the system for a fuel pressure gauge, vent system and a fuel quantity indication.

Figure1.7: Fuel system schematic for light turbine powered helicopter.

Jet Transport Aircraft Fuel Systems

Jet Transport Aircraft Fuel Systems

A large jet transport aircraft, such as the Boeing 727 has a relatively simple fuel system that sup­plies its three engines from three fuel tanks.

Tanks No. 1 and No. 3 are integral tanks, that is, part of the wing is sealed off and fuel is carried in the wing structure itself. Each of these tanks holds about 12,000 pounds of fuel. A fuselage tank consisting of either two or three bladder type fuel cells holds another 24,000 pounds of fuel.

Each of the wing tanks has two 115-volt AC electric boost pumps and the fuselage tank; tank No. 2 has four such pumps.

Each of the three engines may be fed directly from one of the three fuel tanks, or all of the tanks an^d engines may be opened, into a cross-feed manifold.

Fuelling is accomplished by connecting the fuel supply to a single-point fuelling receptacle located under the leading edge of the right wing. Fuel flows from this receptacle through the fuelling and dump manifold into all three tanks through the ap­propriate fuelling valves. When the tanks are com­pletely filled, pressure shutoff valves sense the amount of fuel and shut off the fuelling valve. This prevents the tank being overfilled or damaged. If only a partial fuel load is required, the person fuelling the aircraft can monitor a set of fuel quan­tity gauges at the fuelling station and can shut off the flow al fuel to any tank when the desired level is reached.

The airplane tanks may be refuelled by connect­ing the fuel receiving truck to the manual refuelling valve, closing the engine shutoff valves, and opening the cross-feed valve from the tank to be emptied. The fuel may be cither pumped out of the tank with the boost pumps, or it may be pulled from the tank by suction from the receiving truck. If it Is pulled out by section, it leaves the tank through the boost pump bypass valve.

Fuel may be dumped in-flight by opening the fuel dump valve for the tanks to be dumped and then opening the fuel dump nozzle valve in the wing tip through which the fuel is to leave the airplane. Fuel can be dumped from either wing tip or from both tips at the same time.

There is a fuel dump limit valve in each of the three systems that will shut off the flow if the pressure drops below that. -needed to supply the he engine with adequate fuel. It will also shut off the dump valve when the level in the tank gets down to the preset dump shutoff level. This dump sys­tem is capable of dumping about 1300 pounds of fuel per minute when all of the dump valves are open and the entire boost pumps are operating,

This fuel system has provisions for heating the fuel before it enters the fuel filter if its temperature is low enough for there to be danger of ice forming on the filter.

Figure 1.6: Fuel system for the Boeing 727 transport airplane.

Large Reciprocating Aircraft Fuel Systems

Large Reciprocating Aircraft Fuel Systems

Transport-category aircraft powered by reciprocating engines are rapidly disappearing from the active fleet. One exception seems to be the venerable. Douglas DC -3. This aircraft has seen a working life of more than 50 years and is still being used for passenger and cargo applications. The fuel system installed on the DC--3 is illustrated to figure 1.5 and is typical for aircraft using large radial-type engines.

Fuel is supplied from two resin tanks and two auxiliary tanks mounted in the centre wing section of the airplane. The capacity of each main tank is 202 gallons, and the auxiliary tank holds 200 gallons each. Provisions are made for the installation of from 2 to 8 long-range tanks, each holding 100 gallons. This makes it possible to carry a fuel load of 1604 galleons, in a total of 12 tanks.

The fuel quantity is measured by the liquid meter system which consists of a float as­sembly and a liquid meter tank unit in each tank. These are connected electrically to the fuel gauge on the right instrument panel in the pilots' com­partment. There are two tank selector valves, operated by dial and handle controls in the pilots' compartment. Ordinarily the left hand engine draws fuel from the left tanks, avid the right engine draws fuel from the right tanks, but, by using the selector valves fuel may be supplied from any tank to either engine.

Two hand-operated wobble pumps are used to raise the fuel pressure when starting the engines, or before the engine-driven pumps are in opera­tion. The fuel flows from the wobble bumps through lines to the strainers located in each nacelle, through the engine-driven pumps, and from there, under pressure, into the carburettors. A cross-feed line is connected on the pressure side of each engine-driven pump, and the two cross­-feed valves in this line are operated by a single control in the pilots' compartment. The cross-feed system enables both engines to receive fuel from one engine-driven pump in case either pump fails.

On later model airplanes the wobble pumps are replaced by two electric booster pumps. Each fuel strainer is located in the centre wing near each selector valve. The fuel, therefore, flows from the selector valves, through the strainers, through the booster pumps, through the engine driven fuel pumps into the carburetor. On airplanes equipped with electric booster pumps, there is no cross-feed system. The booster^- pumps will furnish ample pressure and supply for operation of the airplane in case either engine-driven pump fails.

A vapour overflow line connects from the top chamber of the carburetor to the main tanks, and a fuel line from the back of each carburetor operates the fuel pressure gauge in the pilots' compartment. This pressure gauge normally shows from 14 to 16 pounds pressure. On some airplanes a pressure warning switch is installed in they fuel pressure gauge line. When the fuel pres­sure drops below 12 pounds, the switch il­luminates a warning light on tyre instrument panel.

A restricted fitting on the fuel pressure gaugeIine connects to the oil-dilution solenoid. This unit releases fuel into the engine oil system and the propeller feathering oil, to aid in cold weather starting. Another solenoid valve in the fuel pres­sure gauge line releases fuel into the eight upper cylinders of the engines for priming.

Vent lines from each tank vent overboard, and a vapour line connects each main tank with its cor­responding auxiliary tank.

Figure 1.5: DC-3 Fuel system schematic diagram.

Small Multi-Engine Aircraft Fuel Systems

Small Multi-Engine Aircraft Fuel Systems

The diagram in figure 1.4 shows a typical fuel system for a twin-engine airplane using an RSA fuel injection system. This fuel injection system does not return fuel to the tank like the system we have just discussed.

Each wing has two fuel tanks that are connected together and sense as a single tank, and the selec­tor valves allow either engine to operate from the tanks in either wring. From the selector valve, the fuel flows to the fuel filter and then to the electric fuel pump, on to the engine-driven pump, into the fuel injection system and to the cylinders.

The instrumentation for this system consists of the fuel quantity, fuel pressure, and fuel flow gauges. The fuel quantity gauges show the total amount of fuel in the two tanks in each wing. The two fuel pressure gauges show the pressure produced by the fuel pumps. This pressure is measured at the inlet of the fuel metering unit. The fuel flow indicator is a pressure gauge that reads the pressure drop across the fuel injector nozzles and is calibrated in either gallons per hour or in pounds per hour of fuel burned

Figure 1.3: Typical fuel system for a high-performance single-engine airplane using a Teledyne-Continental fuel injection system.

Figure 1.4: Typical fuel system for a twin-engine airplane using an RSA fuel injection systems.

Small Single-Engine Aircraft Fuel Systems

Small Single-Engine Aircraft Fuel Systems

Single-engine aircraft may utilize any of several types of fuel systems, depending upon the fuel metering unit (carburetor or fuel injector) used and whether the aircraft is a high-wing or low-wing design.

a. Gravity-feed Systems

The most simple aircraft fuel system is that found on the small high-wing single-engine train­ing-type airplanes. This type of system is illustrated in figure 1.1. These systems normally use two fuel tanks, one in either wing. The two tank outlets are connected to the selector valve that can draw from either tank individually, or both tanks can feed the engine at the same time. A fourth position on the selector valve turns off all fuel to the engine. Since both tanks can feed the engine at the same time. the space above the fuel in both tanks must be interconnected, and this space vented outside of the airplane. The vent line nor­mally terminates on the underside of the wing where the possibility of fuel siphoning is mini­mized.

After the fuel leaves the selector valve, it passes through the main strainer and on to the carburetor inlet. Fuel for the primer is taken from the main strainer.

Figure 1.1: Typical gravity-feed fuel system for a small single-engine, high-wing airplane.

b. Pump-feed systems

Low wing airplanes cannot use gravity to feed the fuel to the carburetor, and these airplanes use a fuel system similar to that in figure 1.2. The selector valve used in these systems can normally select either tank individually, or shut off all flow to the engine. But they do NOT have a both position, because the pump would pull air from an empty tank rather than fuel from a full tank. After leaving the fuel selector valve, the fuel flows through the main strainer and into the electric fuel pump. You will notice that the engine-driven pump is in parallel with the electric pump. so the fuel can be moved by either pump, and there is no need for a bypass feature to allow one pump to force fuel through the other. In order to assure that both pumps are functioning. note the fuel pressure produced by the electric pump before starting the engine, and then, with the engine running. turn the electric pump off and note the pressure that is produced by the engine driven pump.

The electric pump is used to supply fuel pres­sure for starting the engine and as a backup in case the engine-driven pump should fail and to assure fuel flow when switching from one tank to the other.

Figure 1.2: Typical pump-feed fuel system for a small single-engine, low-wing airplane.

c. High-wing Airplane Using A Fuel Injection System

The fuel injection system requires an engine driven fuel pump, and the system in uses a Teledyne-Continental system that returns part of the fuel from the pump back to the 

fuel tank. This fuel contains any vapours that could block the system, and by purging all of these vapours from the pump and returning them to the tank they cannot cause any problems in the en­gine.

Fuel flows by gravity from the wing tanks through two feed lines, one at the front and me at the rear of the inboard end of each tank, into two small accumulator (reservoir) tanks, and from the bottom of these tanks to the selector valve.

The selector valve directs fuel from the desired reservoir tank to the engine, and at the same time directs the fuel vapour from the engine-driven pump back to the selected reservoir tank. This vapour then returns to the wing tank that supplies the reservoir tank.

Tine electric auxiliary fuel pump picks up the fuel at the discharge of the selector valve and forces it through the strainer and on to the inlet of the engine-driven fuel pump. From the engine driven fuel pump, the fuel flaws to the heel-air control unit where the fuel that is needed for engine operation goes to the cylinders. and all of the excess fuel returns to the inlet side of the pump. Some of the fuel that. is taken into the engine driven pump has vapour in it and this fuel is returned to the selector valve through the fuel return check valve.