## 37 33

1 Casing

2 Impeller

5 Diffuser

6 Shaft

7 Ring, casing

16 Bearing, inboard

18 Bearing, outboard

22 Locknut, bearing

31 Housing, bearing inboard

32 Key, impeller

33 Housing, bearing, outboard 35 Cover, bearing inboard 37 Cover, bearing outboard 40 Deflector

56 Disc or drum, balancing

63 Bushing, stuffing-box

65 Seal, mechanical, stationary element

80 Seal, mechanical, rotating element

83 Stuffing-box

123 Cover, bearing end

Fig. 31-25 Multistage (Radial) Centrifugal Pump. Source: Hydraulic Institute materials. To make calculations easier, all of these quantities are reduced to a coherent format with the same dimensions, know as head.

Head (h) can be expressed in several ways. For example, the specific energy (energy per unit mass) imparted on the medium by the pump is a function of the pressure difference between the outlet and the inlet of the pump and the specific volume of the fluid pumped. Neglecting the velocity and elevation differences between the inlet and outlet of the pump, the head is expressed as the length of a vertical column of the pumped fluid and calculated as:

Fig. 31-26 Radially Split Single-Stage Double-Suction Centrifugal Pump Showing Thrust and Coupling Ends. Source: Goulds Pumps Inc.

Where:

Fig. 31-27 Steam Turbine-Driven Horizontally Split Opposed Impeller Centrifugal Pump. Source: Goulds Pumps Inc.

Where:

Fig. 31-27 Steam Turbine-Driven Horizontally Split Opposed Impeller Centrifugal Pump. Source: Goulds Pumps Inc.

Inlet pressure Outlet pressure Fluid density g = Acceleration due to gravity

The fluid flow, both liquid and gas, through pipe is impeded by frictional resistance that causes a pressure or head loss, which can be evaluated by application of pipe friction equations, which can be found in piping design handbooks (refer to Fanning's or the Darcy Weisbach equation and to Hazen and Williams formula). Consideration must also be given to the roughness of the pipe surface, as friction will vary widely depending on the type of material used. The head losses associated with flow through fittings can also be significant and will vary depending on the size and construction of the fitting. For example, a circular bend with corrugated inner radius will have a friction loss from 1.3 to 1.6 times greater than that of an equivalent smooth elbow or bend. As velocities increase, so do the dynamic losses and the power consumption. Roughness factors and friction losses in standard fittings are also listed in piping design handbooks.

Once the total head is determined, input power may be calculated for a known discharge flow rate as follows:

Where:

P = Power q = Discharge rate

Y = Specific weight of fluid hp = Total head

In English system units, if q is in cf/s, Y is in lbm/cf, hT is in ft of head, and G is in lbm/s, then the theoretical hp, also known as the hydraulic hp requirement, can be expressed as:

qY^T GhT

In SI units, where flow is in L/m, the power input, expressed in bkW, becomes:

qhTSG

60,000rip

To determine the capacity or energy input rating of the driver required to impart to the shaft of the pump the required power, the driver's efficiency (^q) or ability to convert energy into shaft brake power, must also be considered.

### Affinity Laws

Capacity (q) or rate of flow varies directly with the speed of the pump. Thus, the effect of a change of speed from Ni to N2 on pump capacity can be expressed as:

qt N

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