Bombas

L6_Centrifugal pump
The basics
The following functions are present in a centrifugal pump: the flow is induced into the eye of the impeller (r1) , its kinetic energy (and pressure) increase in the impeller itself, and then the flow leaves the impeller at a relatively high speed V2. Diffusion is applied to the flow to increase the static pressure at 3. The operations are summarized in theschematics below:





The impeller turns, communicating a (azimuthal) component to the flow. The flow moving along experiences a centrifugal force, and flows outwards, whereby more fluid enters the impeller at its center. At the tip, the flow has high absolute velocity. The resultant kinetic energy can be transformed into mechanical energy per unit volume (i.e. pressure) in diffusers.Interestingly, the pressure at the vane exit as higher than at the vane inlet. Diffusion occurs in the vanes, for their cross section increases and hence the relative velocity must (for incompressible flows) decrease. The kinetic energy at the impeller exit is converted into pressure times volume (p*v) in the diffuser. Since the specific volume is constant for liquids, the increase in p*v isessentially an increase in pressure The energy transfer (from L3) is:

Then, the energy transfer per unit mass is

L 6-1
If the inlet flow is axial, then Vu1 equals zero, and

The head for the pump is obtained from the first law, steady state, namely
L2-1

For adiabatic flow

the specific energy input to the CV is:

L6-1
The above equation introduces H, the pump head, in ft or m.H is the elevation that the liquid could be raised to. The last equality applies only to inlet axial flow, but in practice it is applied to most flows..






The exit velocity triangle shows that the azimuthal velocity (tangential component of velocity, whirl velocity are other names for it) is given by

L6-2
Becuase Vu2 will actually be lower than the projected value (L6-2) Vu2i, wewill call the head corresponding to this velocity the ideal or theoretical head Hi, namely:

Or, since

Q is volumetric flow rate
b2 is tip depth

is rotational speed, rad/s
then,
L6-3



Head vs. flow for a given rotational speed is typically reported for pumps. Eq. L6-2 shows that increasing 2 tends to decrease the head, if other variables are constant. Yet, the ability of thepump to respond to transient discharge pressure variations increases with increasing 2
Another important equation can be obtained from the inlet velocity triangle, assuming the relative veolcity W1 alinged with the vanes:


L6-4
This is important because the flow rate can be ascertained by measuring a few parameters. , (, b1 and 1)


Example


A centrifugal pump has the followingvariables:
Tip velocity

Inlet circumferencial
velocity

Exit radial
velocity

Impeller dia.

Exit angle

Flow

Density

Calculate the ideal head, torque and power associated with the machine. Give the depth of the impeller.

Head





Torque

L3-7


Power




Impeller exit depth:





Approximation of actual head:


The impeller shown above shows thekey angles 1, with respect to the machine axis, and 2,with respect to the radial direction. These angles are useful, as shown, to project performance, but the flow will not necessarily follow them exactly. Departures result in reduced head values. The complicated flow patterns inside the impeller explain some of the head losses.


Flow inside the impeller and head:

When a flow moves in acircular trajectory, the azimuthal component of the Navier-Stokes equation reads, after simplification:


then, the pressure will rise towards the impeller O.D. Now, the equation above applies only to circular motion, but the flow is moving radially as well. The vanes are communicating an azimuthal component of momentum, which generates a centrifugal force to move the flow radially. The...