Piston pumps theoretical delivery

The theoretical delivery of a piston pump is equal to the total swept volume of the cylinders. The actual delivery may be less than the theoretical value because of leakage past the piston and the valves or because of inertia of the valves. In some cases, however, the actual discharge is greater than theoretical value because the momentum of the liquid in the delivery line and sluggishness in the operation of the delivery valve may result in continued delivery during a portion of the suction stroke. The volumetric efficiency, which is defined as the ratio of the actual discharge to the swept volume, is normally greater than 90 per cent. 

The theoretical fluid displacement of a piston pump equals the total volume swept by the piston on each delivery stroke. Because of leakage past the piston and the valves and failure of the valves to close instantly, this theoretical displacement is not attained in actual practice. The volumetric efficiency, defined as the ratio of the actual displacement to the theoretical displacement, is usually in the range of 70 to 95 percent. 

When a steam pump is used, the pressure of the steam in pounds per unit area times the area of the piston would be the maximum force that could be exerted on the work-delivery piston if the machine were perfect and no friction were involved. However, friction is involved and work must be done on the liquid (or work-receiving fluid) under conditions in which the steam pressure is a finite amount greater than the liquid pressure. The ratio of the pressure theoretically required on the steam piston to the pressure actually exerted by the steam is known as the pressure efficiency or steam-end efficiency. It includes the effects of piston and rod friction, momentum changes in acceleration of the piston and fluid, and leakage of fluid past the piston. The pressure efficiency varies from about 50 percent for small pumps up to 80 percent for large pumps. 

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