The air tends to creep along the blade axially and bank up at the side remote from the inlet .sx To counteract this , either the inlet extremities of the blades are arranged to lag behind the delivery extremities in the direction of rotation , or the diameter at the blades nearest the inlet side should be slightly greater and gradually decrease down to the diameter of the wheel-disc side .sx A further point is the taper of the inlet edge of blades parallel with the axis ; this adds to the efficiency of air entrance .sx For particular duties , other types of wheels are made having the shape of blade at the inlet in the form of a screw propeller , finishing at the periphery as a plain blade ; also the screw-propeller fan is commonly used when large volumes of air are .sx to be displaced against no pressure .sx In this particular design the air flows axially , varying in velocity radially along the blade .sx Its action is similar to that of the air screw for an aeroplane .sx Fan Casings .sx It is usual to express the principal dimensions in terms of the wheel diameter .sx Let D be the diameter of the wheel and D1 the smallest diameter of the fan inlet .sx The capacity is influenced both by blade area or surface and the restriction to flow at the inlet .sx A good compromise is to make D1 not less than 0.625D. Also , it is better to attach a converging conical entrance piece , as shown in fig. 9 .sx Two inlets are sometimes employed where large volumes are dealt with , in which case the impeller has blades attached to either side of the wheel disc .sx The wheel discharge chamber is often referred to as the diffuser or volute casing .sx When a fan is fully loaded , i.e. delivering a full blast , air is given off at a uniform rate per unit length of periphery of wheel .sx There must therefore be a uniform increase in area outside the wheel for the passage of air .sx Two types of housings are commonly employed .sx Arrangement I. An annular space , having a free outlet all round the periphery , surrounds the wheel .sx In this type of casing , known as a diffuser casing , the peripheral area increases with the radius .sx This has the effect of reducing the air velocity and converting it into pressure .sx Also , the surrounding pressure acts radially , and in order that the direction of flow , when leaving the blades , shall be as near radial as possible , backward curvature should be employed .sx The diameter of the diffuser chamber is found from the velocity diagram ( fig. 9 ) , if a final discharge velocity is assumed ( usually about 500 to 1000 ft .sx per minute) .sx The volume passing through is known , and the products of the radial velocity vr2 and peripheral areas must be equal at any part .sx We have then the following equations :sx , where W2 is the width of diffuser chamber at entrance , and W3 is the width of diffuser chamber at exit .sx The width at entrance is usually that of the wheel , and the sides may be radial or slightly divergent or convergent .sx Change in width will have an effect upon the radius r3 for a given discharge velocity .sx In the case of a divergent casing , the angle must not exceed 7 taper .sx Arrangement II , Spiral or Volute Casing .sx With this type of housing .sx the air is collected from the periphery of the wheel before discharge .sx Therefore the airway must be of increasing area .sx The change in area is usually affected by change of curvature of the outer wall by making it of spiral form .sx Fig. 10 shows the general shape of a volute or spiral casing .sx The point a is known as the cut-off point , where the spiral discontinues its approach to the wheel circumference .sx On reaching this point , after one revolution , the wheel has delivered the whole of its contents .sx Commencing the spiral from the point of intersection with the wheel circumference at the tangent drawn parallel to the axis of discharge , its .sx equation will be , where R is the distance from wheel centre to a point on curve corresponding to angle a measured from point of intersection .sx For the common form of multi-blade fan , , where a is in radians .sx In practice the cut-off point is moved back about 300 to allow a little clearance and to permit the nose to be rounded off .sx To do this adds sensibly to the prevention of noise .sx This leaves a small portion of the wheel periphery exposed or uncovered by the spiral , and on this section there will be a tendency for slip or air leak , back through the fan , due to the pressure at the tip being slightly less than at the point of cut-off .sx The practical advantages , however , by retarding the cut-off point warrant the small amount of slippage .sx In the case of a fan having two discharge branches the same spiral may be used , stopping off at 180 , the second being started from this point .sx The linear dimensions and areas of volute will be approximately halved .sx Fans having high tip speeds with forward-curved blades sometimes have a diffuser casing and volute when high efficiency is required ; also a more complete conversion of velocity into pressure is effected with the help of a diverging pipe from the point of cut-off at the volute discharge .sx RECIPROCATING COMPRESSORS .sx In the piston type of compressor the work of compression is done intermittently , one complete cycle being performed per revolution when single acting and two when double acting .sx A volume of air is drawn through automatic or mechanically operated inlet valves into the cylinder as the piston moves outwards ; compression and delivery through other similar valves takes place on the return stroke .sx Piston displacement is the volume swept by the piston on the suction stroke .sx Although not a true measure of the capacity , it forms the base from which the capacities of compressors are compared .sx Delivered capacity is the actual volume of free air ( at atmospheric pressure ) delivered .sx True volumetric efficiency is the ratio of the volume of free air drawn in to the piston-displacement volume .sx This ratio depends largely upon the clearance space and efficiency of valves .sx The clearance space is the total space existing between the piston crown , when at top dead centre , and the cylinder head , including valve ports .sx Its effect on volumetric efficiency is very important , owing to the fact that a maximum pressure remains in the enclosed space after valves close .sx As the piston recedes the volume of compressed air expands approximately isothermally until the pressure falls below that necessary to induce the flow of a fresh charge .sx Referring to fig. 4 , it will be seen that a considerable portion of the piston displacement is thus robbed of its capacity to charge .sx A common figure for clearance volume is about 3 per cent of the displacement for small machines , and about 1 per cent for large machines .sx The apparent volumetric efficiency is represented by the volume up to the point where the expansion line meets the suction-pressure line , divided by the piston-displacement volume .sx It differs from the true efficiency in that the average condition of temperature and pressure in the cylinder at the end of the suction stroke have changed relatively to those of the outside air .sx The mean effective pressure is the average pressure attained throughout the two strokes or per cycle , usually expressed in pounds per square inch units .sx For compression in one cylinder ; for multi-stage compression ; where s is the number of stages or cylinders , n the index of compression which varies from 1.3 to 1.35 , depending upon cylinder design and means of cooling , p1 is the final pressure , and p0 the initial pressure in each cylinder in pounds per square inch .sx Single-stage compressors are built for maximum pressures up to 100 lb .sx per square inch ; two-stage compressors up to 500 lb .sx per square inch ; three-stage compressors up to 1000 lb .sx per square inch .sx Between each stage it is necessary to pass the air through an intercooler in order to extract the heat of compression generated in the preceding cylinder .sx With perfect intercooling , and neglecting the clearance volume , the theoretical horse-powers required to compress air are as follows :sx Single stage :sx ; Two stage :sx ; Three stage :sx ; where p0 , V0 are initial pressure and volume , and p1 is final pressure , the units being cubic feet for volume and pounds per square inch for pressure .sx With perfect intercooling , then , the size or volume of each cylinder should be in inverse proportion to pressure at admission .sx In actual practice the temperature , after passing an intercooler , is slightly higher than the initial temperature of the free air , whilst the exit pressure has fallen below that of the inlet .sx The volume of air delivered by a given compressor at altitude a , compared to that delivered at sea-level , is given by the equation :sx , where P is the gauge pressure in pounds per square inch , and p the barometric pressure in pounds per square inch .sx Although the volume delivered decreases with altitude , the power does not decrease in the same proportion .sx The theoretical power may be computed from the horse-power formulae by substituting for , the ratio of compression remaining the same for a given machine .sx Cooling .sx Injecting water in the form of a spray has been tried as a means of cooling , and compression curves of have been obtained .sx The chief objection to this so-called " wet compression " is the reduced capacity consequent upon the moisture affecting the initial density , and the mechanical auxiliaries .sx Further , because of the time element required to vaporize and .sx mix thoroughly with the incoming air , such machines will not operate efficiently at high speeds .sx External cooling is almost exclusively adopted .sx For the smaller sizes of cylinders the outside walls are ribbed , and radiate the heat to the surrounding atmosphere .sx The larger sizes are water jacketed , giving an average compression .sx The quantity of water necessary is a function of the inlet temperature , a common figure being twice the inlet temperature in degrees F. equals the number of gallons per hour per 100 cubic feet per minute .sx Intercoolers consist of long cylindrical chambers fitted with longitudinal tubes through which water is circulated , the compressed air to be cooled passing around and along the circumference .sx The flow of water and air should be in opposite directions , in order that the coolest air may meet the coolest water .sx A section of a cooler is shown mounted on a compressor in fig. 11 .sx The number of cubic feet of free air per minute per square foot of cooling surface is given as , where ta is the temperature of air leaving , tw that of the water entering , both in degrees F. .sx Valves .sx For high volumetric efficiency , the inlet valves should have a large area of passage with rapid opening and closing to prevent wire-drawing of the air .sx It is also very important that the delivery valves should close quickly , as the leakage back into the cylinder reduces both capacity and efficiency .sx Combination of Valves .sx The most desirable combination of inlet and delivery valves would be to have the inlet valve a mechanically operated one , such as a Corliss , and for the delivery valve to open automatically and close mechanically .sx In many machines a number of small poppet valves working automatically are employed both for inlet and delivery .sx These are fairly efficient and reliable , but are somewhat noisy in operation .sx Another good type commonly used is the plate valve , made of thin tempered steel or bronze .sx These valves are very light , and consequently the inertia forces are small , thus facilitating rapid opening and closing .sx The area through the inlet valves should not be less than 10 per cent of the piston area , and for the delivery 12 per cent .sx These percentages apply to normal piston speeds of 400 ft .sx per minute .sx Higher piston speeds of 800 ft .sx per minute are adopted , in which case the valve areas should be in the order of 13 per cent and 15 per cent .sx