Lesson 14 - Fluid Mechanics End of Unit SAQ

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a)    Describe the principle of operation of a centrifugal pump with reference to Bernoulli’s equation and pump geometry.

b)    Describe the principle of operation of a positive displacement pump.

Response:

a)    A centrifugal pump has an impeller mounted on the end of a horizontal shaft, which is typically driven by an electric motor. The impeller rotates within a stationary casing, which has a gradually increasing section with a single tangential outlet.

Liquid is fed onto the centre of the rapidly rotating impeller and is thrown outwards, with increased kinetic energy, due to the centrifugal force generated by the rotation.

The gradually increasing section of the casing (or stator) reduces the velocity. This is described by the continuity equation below, in which the mass flow rate G is conserved through the casing. For a constant density, the increasing section area A between section 1 and 2 will result in the velocity u reducing.

As the velocity u reduces, we know from Bernoulli’s equation (below) that assuming a constant density, kinetic energy (ρu²/2) will reduce. If we ignore any small change of vertical distance h through the casing, then any reduction in kinetic energy must be compensated by an increase in pressure energy and hence pressure P.

b)    Positive displacement pumps work on the principle of volume entrapment and displacement. This principle is best described with reference to a specific type of positive displacement pump. The reciprocating piston pump is explained here, but you may have chosen another pump to describe.

In the figure below, you can see a cylinder with a reciprocating piston which moves upwards and downwards. The cylinder is fitted with an inlet and an outlet port, each with a valve.

As the piston moves downwards, the inlet valve is open, and the outlet valve is closed. The piston draws in liquid through the inlet port by suction. As the piston changes direction and is driven upwards, the inlet valve is closed, and the outlet valve is opened to allow the piston to pump out liquid under pressure. In this way, you can see that the cylinder and piston, together with the valves, entrap a volume of liquid, and then the piston displaces that volume through the outlet port. The suction and pressure cycles are repeated many times to pump liquid at a particular flow rate.