Piston Displacement

The actual volume of the cylinder that is swept by the piston per minute is piston displacement. It can be calculated from  

Double acting cylinder (sum of head end and crank end displacement) 

In addition, piston displacement and thus throughput can be changed by changing cylinder liners, installing sleeves, or boring the cylinder. 

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V = average gas velocity, fpm Pd = piston displacement per cylinder, ft /min A = total inlet or discharge valve area per cylinder, in. ... 

Calculate the piston displacement using Equation 3.2 and dividing by 1,728 in. per fC to convert the output to cfm. 

Once the inlet and discharge volumetric efficiencies are determined, bottles for the inlet and discharge may be sized. Begin the process of sizing the bottle of interest using the appropriate volumetric efficiency (inlet or discharge) and determine a multiplier from Figure 3-27. Use Equation 3,1, 3.2, or 3.3 to determine the piston displacement. In the calculation. 

Clearance is the volume remaining in a cylinder end when the piston is at the end of its stroke. This is die sum of the volume between the head of the cylinder and the piston, and the volume under tlie valve seats. The total clearance is expressed in percent of the total piston displacement, normally between 4 and 30%. 

The capacity of the cylinder is a function of piston displacement and volumetric efficiency. This is in turn a function of cylinder clearance, compression ratio, and gas properties. 

The flow rate is not directly equal to the piston displacement. Volumetric efficiency is the ratio of actual volumetric flow at inlet tempera-mre and pressure conditions to piston displacement. It is given by ... 

C = cylinder clearance, percent of piston displacement Z5 = compressibility factor at suction, psia Z(j = compressibility factor at discharge, psia k = ratio of specific heats, Cp/C ... 

Using a known piston displacement and efficiency, the gas throughput can be calculated from ... 

Toward the end of the nineteenth centuiy, successful two-stroke engines operating on the Otto cycle were developed by Dugald Clerk, James Robson, Karl Benz, and James Day. In this engine, the intake, combustion, expansion, and exhaust events all occur with but two piston strokes, or one crankshaft revolution. In principle this should double the output of a four-stroke engine of equal piston displacement. However, instead of the intake and exhaust events taking place during sequential strokes of the piston, they occur concurrently while the piston is near BDC. This impairs the ability of the... 

The slip of a pump is fraction or percent loss of capacity relative to theoretical. Slip is (1 — Cvoi), w here e oi is the volumetric efficiency. Volumetric efficiency is the actual liquid pumped (usually considered water) relative to that which should theoretically be pumped based on piston displacement. 

Partial pressure of air in mixture, Ibs/sq in. abs = Absolute intake pressure of pump = Piston displacement, cu ft/min = Partial pressure of non-condensable gas pounds per square inch absolute (or other absolute units)... 

Piston displacement is the actual volume of the cylinder displaced as the piston travels its stroke from the start of the compression (condition (1)) to the end of the stroke (condition (e)) of Figure 12-12 expressed as fF of volume displaced per minute. Displacement values for specific cylinder designs are available from the manufacturers, Table 12-6. Neerken is a useful reference. Reciprocating compressors are usually rated in terms of piston displacement, which is the net volume in ft per minute displaced by the moving piston. Note that the piston does not move through the clearance volume of Figure 12-12 therefore this volume is not displaced during the stroke. 

The displacement of the crank end is less than that of the head end by the volume equivalent to the piston rod displacement. For a multistage unit, the piston displacement is often only given for the first stage. ... 

Percent clearance is the volume % of clearance volume to total actual piston displacement. ... 

For double-acting cylinders, % clearance is based on total clearance volume for both the head end and crank end of the cylinder X 100 divided by the total nel piston displacement. The head and crank end % clearance values will be different due to the presence of the piston rod in the crank end of the cylinder. The % clearance values are available from manufacturers for their cylinders. The values range from about 8% for large 36-in. cylinders to 40% for small 3-and 4-in. cylinders. Each cylinder style is different. 

Volumetric efficiency may be expressed as the ratio of actual cylinder capacity expressed at actual inlet temperature and pressure conditions, divided by the piston displacement. See Figure 12-17B. Values of E, may be read from Figures 12-18A-F for values of R, and Vp. ... 

PD) = compressor cylinder piston displacement in ft /min(cfm). These values can be calculated from known cylinder data or obtained from the respective compressor manufacturer for the specific cylinder in question, operating at the designated rpm. 

The general steps in cylinder selection wiU be outlined. However, actual selection can be accomplished only by referring to a specific manufacturer s piston displacement and the volumetric efficiency of a cylinder. The volumetric efficiency is a function of the compression ratio and k value of gas (both independent of cylinder) and the % clearance, a function of cylinder design. 

Piston displacement (double acting cyl.) = 731 cfm each Piston displacement head end = 374 cfm Piston displacement crank end = 357 cfm Clearance, (cylinder data) = 11.1%... 

In many instances, the design of suction and discharge pulsation dampening drums (or bottles) for reciprocating compressors is based on piston displacement and volumetric efficiency, and this design normally will suffice to reduce peak pulsation to approximately 5% of the line pressure. In special or other cases, experience has shown that operational difficulties (vibrations, meter pulsations, etc.) may indicate that the peak pulse pressure of 5% line pressure is inadequate. Thus, the pressure in pulsation-reduction design selection is... 

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