Question

Demonstrate with the aid of a diagram how the pump system works

Answer 1

Pumps

Rotodynamic Pumps

A rotodynamic pump is a device where mechanical energy is transferred from the rotor to the fluid by the principle of fluid motion through it. The energy of the fluid can be sensed from the pressure and velocity of the fluid at the delivery end of the pump. Therefore, it is essentially a turbine in reverse. Like turbines, pumps are classified according to the main direction of fluid path through them like (i) radial flow or centrifugal, (ii) axial flow and (iii) mixed flow types.

Centrifugal Pumps

The pumps employing centrifugal effects for increasing fluid pressure have been in use for more than a century.The centrifugal pump, by its principle, is converse of the Francis turbine. The flow is radially outward, and the hence the fluid gains in centrifugal head while flowing through it. Because of certain inherent advantages,such as compactness, smooth and uniform flow, low initial cost and high efficiency even at low heads, centrifugal pumps are used in almost all pumping systems. However, before considering the operation of a pump in detail, a general pumping system is discussed as follows.

General Pumping System and the Net Head Developed by a Pump

The word pumping, referred to a hydraulic system commonly implies to convey liquid from a low to a high reservoir. Such a pumping system, in general, is shown in Fig. 33.1. At any point in the system, the elevation or potential head is measured from a fixed reference datum line. The total head at any point comprises pressure head, velocity head and elevation head. For the lower reservoir, the total head at the free surface is $8_1_clip_image002.gif$ and is equal to the elevation of the free surface above the datum line since the velocity and static pressure at A are zero. Similarly the total head at the free surface in the higher reservoir is ( $8_1_clip_image004.gif$) and is equal to the elevation of the free surface of the reservoir above the reference datum.

The variation of total head as the liquid flows through the system is shown in Fig. 33.2. The liquid enters the intake pipe causing a head loss $8_1_clip_image006.gif$ for which the total energy line drops to point B corresponding to a location just after the entrance to intake pipe. The total head at B can be written as

$8_1_clip_image002_0000.gif$

As the fluid flows from the intake to the inlet flange of the pump at elevation $8_1_clip_image002_0001.gif$ the total head drops further to the point C (Figure 33.2) due to pipe friction and other losses equivalent to $8_1_clip_image002_0016.gif$ . The fluid then enters the pump and gains energy imparted by the moving rotor of the pump. This raises the total head of the fluid to a point D (Figure 33.2) at the pump outlet (Figure 33.1).

In course of flow from the pump outlet to the upper reservoir, friction and other losses account for a total head loss or$8_1_clip_image002_0017.gif$ down to a point E . At E an exit loss $8_1_clip_image008.gif$ occurs when the liquid enters the upper reservoir, bringing the total heat at point F (Figure 33.2) to that at the free surface of the upper reservoir. If the total heads are measured at the inlet and outlet flanges respectively, as done in a standard pump test, then

E F p./pg p./pg 2 Reference datum ^

Figure 33.1 A general pumping system

EL Va HAIA B in

Figure 33.2 Change of head in a pumping system

Total inlet head to the pump = $8_1_clip_image002_0002.gif$

Total outlet head of the pump = $8_1_clip_image004_0001.gif$

where $8_1_clip_image006_0001.gif$ and $8_1_clip_image008_0000.gif$ are the velocities in suction and delivery pipes respectively.

Therefore, the total head developed by the pump,

$8_1_clip_image002_0004.gif$	(33.1)

The head developed H is termed as manometric head . If the pipes connected to inlet and outlet of the pump are of same diameter, $8_1_clip_image002_0005.gif$ and therefore the head developed or manometric head H is simply the gain in piezometric pressure head across the pump which could have been recorded by a manometer connected between the inlet and outlet flanges of the pump. In practice, ( $8_1_clip_image004_0003.gif$) is so small in comparison to $8_1_clip_image006_0003.gif$ that it is ignored. It is therefore not surprising o find that the static pressure head across the pump is often used to describe the total head developed by the pump. The vertical distance between the two levels in the reservoirs $8_1_clip_image008_0002.gif$ is known as static head or static lift. Relationship between $8_1_clip_image008_0003.gif$, the static head and H , the head developed can be found out by applying Bernoulli's equation between A and C and between D and F (Figure 33.1) as follows:

$8_1_clip_image002_0013.gif$	(33.2)

Between D and F ,

og 2g	(33.3)

substituting $8_1_clip_image002_0008.gif$ from Eq. (33.2) into Eq. (33.3), and then with the help of Eq. (33.1),

we can write

$8_1_clip_image002_0022.gif$

	H +Σ losses	(33.4)

Therefore, we have, the total head developed by the pump = static head + sum of all the losses